N. Ivanichok, O. Ivanichok, B. Rachiy, P. Kolkovskyi, I. Budzulyak, V. Kotsyubynsky, V. Boychuk, L. Khrushch
In this work, we have obtained a nanoporous carbon material (CM) from walnut shells using the method of thermal carbonization. Moreover, the in uence of the carbonization temperature of the raw material on the electrical conductivity of the CM obtained by Raman, infrared (IR), and impedance spectroscopy has been investigated. Consequently, to analyze the evolution of the electrical conductivity of the material with an increase in the carbonization temperature, the theory of percolation has been applied.
{"title":"Effect of the carbonization temperature of plant biomass on the structure, surface condition and electrical conductive properties of carbon nanoporous material","authors":"N. Ivanichok, O. Ivanichok, B. Rachiy, P. Kolkovskyi, I. Budzulyak, V. Kotsyubynsky, V. Boychuk, L. Khrushch","doi":"10.30970/jps.25.3801","DOIUrl":"https://doi.org/10.30970/jps.25.3801","url":null,"abstract":"In this work, we have obtained a nanoporous carbon material (CM) from walnut shells using the method of thermal carbonization. Moreover, the in uence of the carbonization temperature of the raw material on the electrical conductivity of the CM obtained by Raman, infrared (IR), and impedance spectroscopy has been investigated. Consequently, to analyze the evolution of the electrical conductivity of the material with an increase in the carbonization temperature, the theory of percolation has been applied.","PeriodicalId":43482,"journal":{"name":"Journal of Physical Studies","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83161833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
On the base of a 1D Shr"{o}dinger equation the non-linear first-order differential equation (Ricatti type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for a case of a single rectangular barrier. Both the scattering and the bound states problem were reformulated in terms of a quantum wave impedance and its application for solving both these problems was considered. The expressions for a reflection and a transmission coefficient were found on the base of a quantum wave impedance approach.
{"title":"Reformulation of transmission and reflection problems in terms of quantum wave impedance function","authors":"O. Hryhorchak","doi":"10.30970/jps.25.4001","DOIUrl":"https://doi.org/10.30970/jps.25.4001","url":null,"abstract":"On the base of a 1D Shr\"{o}dinger equation the non-linear first-order differential equation (Ricatti type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for a case of a single rectangular barrier. Both the scattering and the bound states problem were reformulated in terms of a quantum wave impedance and its application for solving both these problems was considered. The expressions for a reflection and a transmission coefficient were found on the base of a quantum wave impedance approach.","PeriodicalId":43482,"journal":{"name":"Journal of Physical Studies","volume":"150 4 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80384746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The two-particle models in de Sitter space-time with time-asymmetric retarded-advanced interactions are constructed. Particular cases of the field-type electromagnetic and scalar interactions are considered. The manifestly covariant descriptions of the models within the Lagrangian and Hamiltonian formalisms with constraints are proposed. It is shown that the models are de Sitter-invariant and integrable. An explicit solution of equations of motion is derived in quadratures by means of projection operator technique.
{"title":"Solvable two-particle systems with time-asymmetric interactions in de Sitter space","authors":"A. Duviryak","doi":"10.30970/jps.26.3002","DOIUrl":"https://doi.org/10.30970/jps.26.3002","url":null,"abstract":"The two-particle models in de Sitter space-time with time-asymmetric retarded-advanced interactions are constructed. Particular cases of the field-type electromagnetic and scalar interactions are considered. The manifestly covariant descriptions of the models within the Lagrangian and Hamiltonian formalisms with constraints are proposed. It is shown that the models are de Sitter-invariant and integrable. An explicit solution of equations of motion is derived in quadratures by means of projection operator technique.","PeriodicalId":43482,"journal":{"name":"Journal of Physical Studies","volume":"26 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74476700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S. Sveleba, I. Katerynchuk, I. Kuno, I. Karpa, O. Semotyuk
The Fourier spectra of the incommensurate modulation and the dependence of the wave vector (q) of the incommensurate (IC) superstructure on the magnitude of the anisotropic interaction described by the Dzialoszynski invariant (K) and the long-range interaction (T) are investigated. Fourier spectra in di(cid:27)erent modulation modes of incommensurate superstructure analyzed. The calculation of the spatial changes of the amplitude and phase of the order parameter was performed by the numerical BDF (Backward Di(cid:27)erentiation Formula) method and was performed in the Python environment using the SciPy, JiTCODE libraries according to the method described in the paper. The parameters T and K, which are responsible for the long-range and anisotropic interactions, respectively, in the (cid:28)rst approximation well describe the behavior of the wave vector of the IC modulation, and its modes. The emergence of IC modulation is accompanied by the appearance of an unstable chaotic state in the case of a nonzero value of the anisotropic interaction. The increase in the value of the anisotropic interaction in the IC phase is accompanied by a change in both the frequency of existing oscillations and the magnitude of their contribution to the formation of a wave of the incommensurate modulation, causing a change in the IC modulation regime. The transition from the one mode to another is continuous. The modes themselves are determined by the domination of the contribution of the respective oscillation frequencies. The whole spectrum of possible frequencies arises at the modulation wave origin. With an increase of the anisotropic interaction, their harmonics emerge and their contribution is redistributed.
{"title":"The dependence of the Fourier spectrum of oscillations of the amplitude function of the incommensurate superstructure on the magnitude of the anisotropic interaction interacting with Dzialoszynski invariant","authors":"S. Sveleba, I. Katerynchuk, I. Kuno, I. Karpa, O. Semotyuk","doi":"10.30970/jps.24.4603","DOIUrl":"https://doi.org/10.30970/jps.24.4603","url":null,"abstract":"The Fourier spectra of the incommensurate modulation and the dependence of the wave vector (q) of the incommensurate (IC) superstructure on the magnitude of the anisotropic interaction described by the Dzialoszynski invariant (K) and the long-range interaction (T) are investigated. Fourier spectra in di(cid:27)erent modulation modes of incommensurate superstructure analyzed. The calculation of the spatial changes of the amplitude and phase of the order parameter was performed by the numerical BDF (Backward Di(cid:27)erentiation Formula) method and was performed in the Python environment using the SciPy, JiTCODE libraries according to the method described in the paper. The parameters T and K, which are responsible for the long-range and anisotropic interactions, respectively, in the (cid:28)rst approximation well describe the behavior of the wave vector of the IC modulation, and its modes. The emergence of IC modulation is accompanied by the appearance of an unstable chaotic state in the case of a nonzero value of the anisotropic interaction. The increase in the value of the anisotropic interaction in the IC phase is accompanied by a change in both the frequency of existing oscillations and the magnitude of their contribution to the formation of a wave of the incommensurate modulation, causing a change in the IC modulation regime. The transition from the one mode to another is continuous. The modes themselves are determined by the domination of the contribution of the respective oscillation frequencies. The whole spectrum of possible frequencies arises at the modulation wave origin. With an increase of the anisotropic interaction, their harmonics emerge and their contribution is redistributed.","PeriodicalId":43482,"journal":{"name":"Journal of Physical Studies","volume":"38 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84853147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Dendebera, A. Zhyshkovych, T. Malyi, L. Demkiv, N. Gloskovska, T. Demkiv, V. Vistovskyy, A. Gektin, A. Voloshinovskii
Film polymer composite scintillators based on scintillation polystyrene with n-terphenyl and POPOP activators and loaded LaF 3 nanoparticles have been developed for the registration of ionizing radiation. LaF 3 nanoparticles were obtained through precipitation involving ion substitution from LaCl 3 water and water-alcohol solution with the addition of NH 4 F solution. The spectral and kinetic properties of polymer nanocomposites under X-ray irradiation have been studied. It was found that the e(cid:30)ciency of the ionizing radiation detection for a polystyrene composite with loaded non-luminescence LaF 3 nanoparticles increases by an order of magnitude compared to the e(cid:30)ci-ency of a polystyrene scintillator without nanoparticles, maintaining the spectral composition of the polystyrene scintillator radiation and its speed was 3 ns. It is proposed that the main mechanism of the scintillation generation is the excitation of polystyrene matrix by electrons that escape from the nanoparticle by the mechanism of photoe(cid:27)ect under the in(cid:29)uence of
{"title":"Polystyrene composites with loaded LaF3 nanoparticles for registration of ionizing radiation","authors":"M. Dendebera, A. Zhyshkovych, T. Malyi, L. Demkiv, N. Gloskovska, T. Demkiv, V. Vistovskyy, A. Gektin, A. Voloshinovskii","doi":"10.30970/jps.24.4709","DOIUrl":"https://doi.org/10.30970/jps.24.4709","url":null,"abstract":"Film polymer composite scintillators based on scintillation polystyrene with n-terphenyl and POPOP activators and loaded LaF 3 nanoparticles have been developed for the registration of ionizing radiation. LaF 3 nanoparticles were obtained through precipitation involving ion substitution from LaCl 3 water and water-alcohol solution with the addition of NH 4 F solution. The spectral and kinetic properties of polymer nanocomposites under X-ray irradiation have been studied. It was found that the e(cid:30)ciency of the ionizing radiation detection for a polystyrene composite with loaded non-luminescence LaF 3 nanoparticles increases by an order of magnitude compared to the e(cid:30)ci-ency of a polystyrene scintillator without nanoparticles, maintaining the spectral composition of the polystyrene scintillator radiation and its speed was 3 ns. It is proposed that the main mechanism of the scintillation generation is the excitation of polystyrene matrix by electrons that escape from the nanoparticle by the mechanism of photoe(cid:27)ect under the in(cid:29)uence of","PeriodicalId":43482,"journal":{"name":"Journal of Physical Studies","volume":"77 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73029253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
V. Kapustianyk , Yu. Chornii , S. Semak Ivan Franko National University of Lviv, Department of Physics, 50, Drahomanov St., Lviv, UA 79005, Ukraine, Ivan Franko National University of Lviv, Scienti c-Technical and Educational Center of Low-Temperature Studies, 50, Drahomanov St., Lviv, UA 79005, Ukraine (Received 01 November 2020; in nal form 18 November 2020; accepted 24 November 2020; published online 21 December 2020)
V. Kapustianyk, Yu。Lviv Ivan Franko国立大学物理系，50,Drahomanov St，利沃夫，UA 79005，乌克兰;Lviv Ivan Franko国立大学低温研究科技与教育中心，50,Drahomanov St，利沃夫，UA 79005，乌克兰(收到2020年11月1日;最终形式为2020年11月18日;2020年11月24日接受;2020年12月21日在线发布)
{"title":"Thermochromic properties of nano- and microcomposites based on (NH2(C2H5)2)2CuCl4 crystals","authors":"V. Kapustianyk, Yu Chornii, S. Semak","doi":"10.30970/jps.24.4707","DOIUrl":"https://doi.org/10.30970/jps.24.4707","url":null,"abstract":"V. Kapustianyk , Yu. Chornii , S. Semak Ivan Franko National University of Lviv, Department of Physics, 50, Drahomanov St., Lviv, UA 79005, Ukraine, Ivan Franko National University of Lviv, Scienti c-Technical and Educational Center of Low-Temperature Studies, 50, Drahomanov St., Lviv, UA 79005, Ukraine (Received 01 November 2020; in nal form 18 November 2020; accepted 24 November 2020; published online 21 December 2020)","PeriodicalId":43482,"journal":{"name":"Journal of Physical Studies","volume":"32 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86997161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Viscosity, electrical conductivity and thermoelectric power of Cu 33.3Bi 33.3Sn, Cu 25Bi 25Sn 25In, Cu 20Bi 20Sn 20In 20Pb and Cu 20Bi 20Sn 20Ga 20Pb liquid alloys of equiatomic concentrations, which are components of model multicomponent high-entropy alloys, have been studied experimentally. Based on the obtained results, the activation energy of the viscous ow and the entropy of mixing were calculated. The negative values of the entropy of mixing suggest a structural ordering in the system.
{"title":"Thermophysical properties of multicomponent model high-entropy melts","authors":"M. Dufanets, V. Sklyarchuk, Y. Plevachuk","doi":"10.30970/jps.24.4602","DOIUrl":"https://doi.org/10.30970/jps.24.4602","url":null,"abstract":"Viscosity, electrical conductivity and thermoelectric power of Cu 33.3Bi 33.3Sn, Cu 25Bi 25Sn 25In, Cu 20Bi 20Sn 20In 20Pb and Cu 20Bi 20Sn 20Ga 20Pb liquid alloys of equiatomic concentrations, which are components of model multicomponent high-entropy alloys, have been studied experimentally. Based on the obtained results, the activation energy of the viscous ow and the entropy of mixing were calculated. The negative values of the entropy of mixing suggest a structural ordering in the system.","PeriodicalId":43482,"journal":{"name":"Journal of Physical Studies","volume":"20 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91346951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
signals explored. The power spectrum analysis of real pseudorandom signals by the value of the relaxation time tau makes it possible to hypothesize that every real system (cid:16)noise(cid:17) has its own colored noise in its own way. The coloring degree can be estimated by the tau parameter, which is individual for each system. If this hypothesis proves to be correct, then the system can be identi(cid:28)ed by a predestined relaxation time.
{"title":"Evaluation of the difference of pseudorandom signal from white noise using a parameter of energy spectrum model of the signal","authors":"Z. Kolodiy, J. Z. Zvizlo","doi":"10.30970/jps.24.2003","DOIUrl":"https://doi.org/10.30970/jps.24.2003","url":null,"abstract":"signals explored. The power spectrum analysis of real pseudorandom signals by the value of the relaxation time tau makes it possible to hypothesize that every real system (cid:16)noise(cid:17) has its own colored noise in its own way. The coloring degree can be estimated by the tau parameter, which is individual for each system. If this hypothesis proves to be correct, then the system can be identi(cid:28)ed by a predestined relaxation time.","PeriodicalId":43482,"journal":{"name":"Journal of Physical Studies","volume":"6 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74337200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The limb solar (cid:29)are of 17 July 1981 is studied according to the observations carried out with the Echelle spectrograph of a horizontal solar telescope of the Astronomical Observatory of Taras Shevchenko National University of Kiev. For 8 h 17 m UT, close to the (cid:29)ash phase, the I ± V pro(cid:28)les of the K Ca II 3933.7 (cid:6)A and He I 4471.5 (cid:6)A lines are analyzed. At the indicated moment, these lines had two components of emission, narrow and wide, which were mutually shifted on 1.8(cid:21)2 (cid:6)A. The narrow component had a full half-width of 0.24 (cid:6)A in the K Ca II line and 0.34 (cid:6)A in the He I line. The wide component had the full half-widths of 3.3 (cid:6)A and 4.1 (cid:6)A, respectively, for these lines. The magnetic (cid:28)eld magnitude in the (cid:29)are, measured by splitting the narrow component, varies in the picture plane and reaches 1300 ± 200 G for the K Ca II line and 2100 ± 200 G for the He I line. Such features are found at the altitudes of about 10(cid:21)14 Mm above the level of the photosphere. It is important to note that the true values of the local magnetic (cid:28)elds in the (cid:29)are could be even larger, since the obtained results represent a longitudinal component of the magnetic (cid:28)eld, with the assumption that the (cid:28)lling factor equals unity. On the basis of the comparison of the Doppler widths of the narrow component in the two lines under study, the following estimations of kinetic temperature and turbulent velocity were obtained: T = 17000 ± 1000 K, and ξ turb = 10 . 8 ± 0 . 3 km/sec.
根据基辅塔拉斯舍甫琴科国立大学天文台水平太阳望远镜梯队摄谱仪的观测资料，研究了1981年7月17日的太阳翼(cid:29)。在接近(cid:29)灰分相8 h 17 m时，分析了kca II 3933.7 (cid:6)A和He I 4471.5 (cid:6)A谱线的I±V pro(cid:28)les。在指定时刻，这些谱线有窄谱线和宽谱线两个发射分量，它们在1.8(cid:21)2 (cid:6)A上相互位移。窄组分的全半宽分别为0.24 (cid:6) a和0.34 (cid:6) a。宽组分的全半宽分别为3.3 (cid:6)A和4.1 (cid:6)A。在(cid:29)中的磁场(cid:28)，通过拆分窄分量测量，在图像平面上变化，K - Ca - II线达到1300±200 G, He - I线达到2100±200 G。这些特征出现于光球水平以上约10(cid:21)14毫米的高度。重要的是要注意，(cid:29)中的局部磁(cid:28)场的真实值可能更大，因为所获得的结果表示磁(cid:28)场的纵向分量，假设(cid:28) ling因子等于1。通过比较研究中两条线窄分量的多普勒宽度，得到了动力学温度和湍流速度的估计:T = 17000±1000 K， ξ turb = 10。8±0。3公里/秒。
{"title":"Line profiles and magnetic fields in the limb solar flare of July 17, 1981. Preliminary results","authors":"V. Lozitsky, I. Yakovkin, N. Lozitska","doi":"10.30970/jps.24.2901","DOIUrl":"https://doi.org/10.30970/jps.24.2901","url":null,"abstract":"The limb solar (cid:29)are of 17 July 1981 is studied according to the observations carried out with the Echelle spectrograph of a horizontal solar telescope of the Astronomical Observatory of Taras Shevchenko National University of Kiev. For 8 h 17 m UT, close to the (cid:29)ash phase, the I ± V pro(cid:28)les of the K Ca II 3933.7 (cid:6)A and He I 4471.5 (cid:6)A lines are analyzed. At the indicated moment, these lines had two components of emission, narrow and wide, which were mutually shifted on 1.8(cid:21)2 (cid:6)A. The narrow component had a full half-width of 0.24 (cid:6)A in the K Ca II line and 0.34 (cid:6)A in the He I line. The wide component had the full half-widths of 3.3 (cid:6)A and 4.1 (cid:6)A, respectively, for these lines. The magnetic (cid:28)eld magnitude in the (cid:29)are, measured by splitting the narrow component, varies in the picture plane and reaches 1300 ± 200 G for the K Ca II line and 2100 ± 200 G for the He I line. Such features are found at the altitudes of about 10(cid:21)14 Mm above the level of the photosphere. It is important to note that the true values of the local magnetic (cid:28)elds in the (cid:29)are could be even larger, since the obtained results represent a longitudinal component of the magnetic (cid:28)eld, with the assumption that the (cid:28)lling factor equals unity. On the basis of the comparison of the Doppler widths of the narrow component in the two lines under study, the following estimations of kinetic temperature and turbulent velocity were obtained: T = 17000 ± 1000 K, and ξ turb = 10 . 8 ± 0 . 3 km/sec.","PeriodicalId":43482,"journal":{"name":"Journal of Physical Studies","volume":"31 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79330908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we presented and reviewed a formalism that plays a central role in most of the investigations concerning noncommutative geometry. We presented existing methods that successfully allow us to utilize and apply the noncommutativity of phase-space in both quantum mechanics and quantum (cid:28)eld theory. In particular, we brie(cid:29)y explained the Weyl quantization, the Moyal(cid:21)Weyl product, the Bopp-shift transformations, and the Seiberg(cid:21)Witten maps.
{"title":"On the noncommutative geometry in quantum mechanics","authors":"Ilyas Haouam","doi":"10.30970/jps.24.2002","DOIUrl":"https://doi.org/10.30970/jps.24.2002","url":null,"abstract":"In this paper, we presented and reviewed a formalism that plays a central role in most of the investigations concerning noncommutative geometry. We presented existing methods that successfully allow us to utilize and apply the noncommutativity of phase-space in both quantum mechanics and quantum (cid:28)eld theory. In particular, we brie(cid:29)y explained the Weyl quantization, the Moyal(cid:21)Weyl product, the Bopp-shift transformations, and the Seiberg(cid:21)Witten maps.","PeriodicalId":43482,"journal":{"name":"Journal of Physical Studies","volume":"98 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80750578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：