We propose a procedure to generalize the Husimi distribution to systems with continuous spectrum. We start examining a pioneering work, by Gazeau and Klauder, where the concept of coherent states for systems with disc...We propose a procedure to generalize the Husimi distribution to systems with continuous spectrum. We start examining a pioneering work, by Gazeau and Klauder, where the concept of coherent states for systems with discrete spectrum was extended to systems with continuous one. In the present article, we see the Husimi distribution as a representation of the density operator in terms of a basis of coherent states. There are other ways to obtain it, but we do not consider here. We specially discuss the problem of the continuous harmonic oscillator.展开更多
The Dimensional Regularization technique of Bollini and Giambiagi (BG) [Phys. Lett. <strong>B 40</strong>, 566 (1972);Il Nuovo Cim. <strong>B 12</strong>, 20 (1972);Phys. Rev. <strong>D 5...The Dimensional Regularization technique of Bollini and Giambiagi (BG) [Phys. Lett. <strong>B 40</strong>, 566 (1972);Il Nuovo Cim. <strong>B 12</strong>, 20 (1972);Phys. Rev. <strong>D 53</strong>, 5761 (1996)] cannot be employed for <em>all</em> Schwartz Tempered Distributions Explicitly Lorentz Invariant (STDELI) S<span style="white-space:nowrap;"><sup><span style="white-space:normal;">′</span></sup><sub style="margin-left:-7px;">L</sub></span>. We lifted such limitation in [J. Phys. Comm. <strong>2</strong> 115029 (2018)], which opens new QFT possibilities, centering in the use of STDELI that allows one to obtain a product in a ring with zero divisors. This in turn, overcomes all problems regrading QFT infinities. We provide here three examples of the application of our STDELI-extension to quantum field theory (A) the exact evaluation of an electron’s self energy to one loop, (B) the exact evaluation of QED’s vacuum polarization, and C) the <img src="Edit_a42ec50a-a738-42b3-beaa-ce9730d18cdb.png" alt="" />theory for six dimensions, that is non-renormalizable.展开更多
In this work we will use a recently developed non relativistic (NR) quantization methodology that successfully overcomes troubles with infinities that plague non-renormalizable quantum field theories (QFTs). The ensui...In this work we will use a recently developed non relativistic (NR) quantization methodology that successfully overcomes troubles with infinities that plague non-renormalizable quantum field theories (QFTs). The ensuing methodology is here applied to Newton’s gravitation potential. We employ here the concomitant mathematical apparatus to formulate the NR QFT discussed in the well known classical text-book by Fetter and Walecka. We emphasize the fact that we speak of non relativistic QFT. This is so because we appeal to Newton’s gravitational potential, while in a relativistic QFT one does not employ potentials. Our main protagonist is the notion of propagator. This notion is of the essence in non relativistic quantum field theory (NR-QFT). Indeed, propagators are indispensable tools for both nuclear physics and condensed matter theory, among other disciplines. In the present work we deal with propagators for both fermions and bosons.展开更多
We discuss the process of equilibrium’s attainment in an interacting many-fermions system linked to a heat reservoir, whose temperature <em>T</em> is subject to a short-time disturbance of total duration ...We discuss the process of equilibrium’s attainment in an interacting many-fermions system linked to a heat reservoir, whose temperature <em>T</em> is subject to a short-time disturbance of total duration 2<span style="white-space:nowrap;"><em>τ</em>.</span> In this time-interval, its temperature increases up to a maximum value , cooling off afterward (also gradually) to its original value T<sub><em>M</em></sub>. The process is described by a typical master equation that leads eventually to equilibration. We discuss how the equilibration process depends upon 1) the system’s fermion-number, 2) the fermion-fermion interaction’s strength <em>V</em>, 3) the disturbance duration <span style="white-space:nowrap;"><span style="white-space:nowrap;">2<span style="white-space:nowrap;"><em>τ</em></span></span></span><em></em>, and finally 4) the maximum number of equations <em>N</em> of the master equation.展开更多
In many interesting physical examples, the partition function is divergent, as first pointed out in 1924 by Fermi (for the hydrogen-atom case). Thus, the usual toolbox of statistical mechanics becomes unavailable, not...In many interesting physical examples, the partition function is divergent, as first pointed out in 1924 by Fermi (for the hydrogen-atom case). Thus, the usual toolbox of statistical mechanics becomes unavailable, notwithstanding the well-known fact that the pertinent system may appear to be in a thermal steady state. We tackle and overcome these difficulties hereby appeal to firmly established but not too well-known mathematical recipes and obtain finite values for a typical divergent partition function, that of a Brownian particle in an external field. This allows not only for calculating thermodynamic observables of interest, but for also instantiating other kinds of statistical mechanics’ novelties.展开更多
We study the dependence of the of microstates number (for free fermions-bosons) as a function of the volume-size in quantum statistics and fermions, and show then that fermions can not be accommodated in arbitrarily s...We study the dependence of the of microstates number (for free fermions-bosons) as a function of the volume-size in quantum statistics and fermions, and show then that fermions can not be accommodated in arbitrarily small volumes <em>V</em>. A minimum <em>V</em> = <em>V</em><sub>min</sub> for that purpose is determined. Fermions can not exist for <em style="white-space:normal;">V</em><span style="white-space:normal;"> < </span><em style="white-space:normal;">V</em><sub style="white-space:normal;">min</sub>. This fact might have something to do with inflation. More precisely, in order to accommodate N fermions in a Slater determinant, we need a minimum radius, which is a consequence of the Pauli principle. This does not happen for bosons. As a consequence, extrapolating this statistical feature to a cosmological setting, we are able to “predict” a temperature-value for the final-stage of the inflationary period. This value agrees with current estimates.展开更多
I.EXECUTIVE SUMMARY next-generation,high-intensity electron-positron collider"Higgs factory",such as the Circular Electron-Positron Collider(CEPC),is among the highest priorities for the global high-energy c...I.EXECUTIVE SUMMARY next-generation,high-intensity electron-positron collider"Higgs factory",such as the Circular Electron-Positron Collider(CEPC),is among the highest priorities for the global high-energy collider physics community.The CEPC can provide unprecedented opportunities for making fundamental discoveries and providing decisive insights in the quest for a"New Standard Model(SM)"of nature's fundamental interactions.The CEPC could:·Identify the origin of matter,especially the mechanism related to the first-order phase transition in the early Universe,which could produce a detectable gravitational wave signal.展开更多
基金partial financial support by FONDECYT, under Grant No. 1080487
文摘We propose a procedure to generalize the Husimi distribution to systems with continuous spectrum. We start examining a pioneering work, by Gazeau and Klauder, where the concept of coherent states for systems with discrete spectrum was extended to systems with continuous one. In the present article, we see the Husimi distribution as a representation of the density operator in terms of a basis of coherent states. There are other ways to obtain it, but we do not consider here. We specially discuss the problem of the continuous harmonic oscillator.
文摘The Dimensional Regularization technique of Bollini and Giambiagi (BG) [Phys. Lett. <strong>B 40</strong>, 566 (1972);Il Nuovo Cim. <strong>B 12</strong>, 20 (1972);Phys. Rev. <strong>D 53</strong>, 5761 (1996)] cannot be employed for <em>all</em> Schwartz Tempered Distributions Explicitly Lorentz Invariant (STDELI) S<span style="white-space:nowrap;"><sup><span style="white-space:normal;">′</span></sup><sub style="margin-left:-7px;">L</sub></span>. We lifted such limitation in [J. Phys. Comm. <strong>2</strong> 115029 (2018)], which opens new QFT possibilities, centering in the use of STDELI that allows one to obtain a product in a ring with zero divisors. This in turn, overcomes all problems regrading QFT infinities. We provide here three examples of the application of our STDELI-extension to quantum field theory (A) the exact evaluation of an electron’s self energy to one loop, (B) the exact evaluation of QED’s vacuum polarization, and C) the <img src="Edit_a42ec50a-a738-42b3-beaa-ce9730d18cdb.png" alt="" />theory for six dimensions, that is non-renormalizable.
文摘In this work we will use a recently developed non relativistic (NR) quantization methodology that successfully overcomes troubles with infinities that plague non-renormalizable quantum field theories (QFTs). The ensuing methodology is here applied to Newton’s gravitation potential. We employ here the concomitant mathematical apparatus to formulate the NR QFT discussed in the well known classical text-book by Fetter and Walecka. We emphasize the fact that we speak of non relativistic QFT. This is so because we appeal to Newton’s gravitational potential, while in a relativistic QFT one does not employ potentials. Our main protagonist is the notion of propagator. This notion is of the essence in non relativistic quantum field theory (NR-QFT). Indeed, propagators are indispensable tools for both nuclear physics and condensed matter theory, among other disciplines. In the present work we deal with propagators for both fermions and bosons.
文摘We discuss the process of equilibrium’s attainment in an interacting many-fermions system linked to a heat reservoir, whose temperature <em>T</em> is subject to a short-time disturbance of total duration 2<span style="white-space:nowrap;"><em>τ</em>.</span> In this time-interval, its temperature increases up to a maximum value , cooling off afterward (also gradually) to its original value T<sub><em>M</em></sub>. The process is described by a typical master equation that leads eventually to equilibration. We discuss how the equilibration process depends upon 1) the system’s fermion-number, 2) the fermion-fermion interaction’s strength <em>V</em>, 3) the disturbance duration <span style="white-space:nowrap;"><span style="white-space:nowrap;">2<span style="white-space:nowrap;"><em>τ</em></span></span></span><em></em>, and finally 4) the maximum number of equations <em>N</em> of the master equation.
文摘In many interesting physical examples, the partition function is divergent, as first pointed out in 1924 by Fermi (for the hydrogen-atom case). Thus, the usual toolbox of statistical mechanics becomes unavailable, notwithstanding the well-known fact that the pertinent system may appear to be in a thermal steady state. We tackle and overcome these difficulties hereby appeal to firmly established but not too well-known mathematical recipes and obtain finite values for a typical divergent partition function, that of a Brownian particle in an external field. This allows not only for calculating thermodynamic observables of interest, but for also instantiating other kinds of statistical mechanics’ novelties.
文摘We study the dependence of the of microstates number (for free fermions-bosons) as a function of the volume-size in quantum statistics and fermions, and show then that fermions can not be accommodated in arbitrarily small volumes <em>V</em>. A minimum <em>V</em> = <em>V</em><sub>min</sub> for that purpose is determined. Fermions can not exist for <em style="white-space:normal;">V</em><span style="white-space:normal;"> < </span><em style="white-space:normal;">V</em><sub style="white-space:normal;">min</sub>. This fact might have something to do with inflation. More precisely, in order to accommodate N fermions in a Slater determinant, we need a minimum radius, which is a consequence of the Pauli principle. This does not happen for bosons. As a consequence, extrapolating this statistical feature to a cosmological setting, we are able to “predict” a temperature-value for the final-stage of the inflationary period. This value agrees with current estimates.
基金the Natural Science Foundation of China(NSFC)(11905162,12035008,12075097,12075123,12090060,12090064,12105248,12135006,12175039,12205227,12205312,12205387,12205171,12235008,12321005,12235001,12305094,12305115,12335005,12375091,12375094,12375096,11975129,12375194,12447167,12475094,12475101,12475106,12475111,12425506,12375101,12405119,12405101,12505121,12135007,12175218,12075213,12335005,12175243,12533001,12125503,12305103,12505120,12575099,12505122,12342502,12575106,12147214,W2432006,W2441004)the National Key R&D Program of China(2024YFA1610603)+22 种基金the China Postdoctoral Science Foundation(2023M732255,2025M773403,GZC20231613)the Natural Science Foundation of Jiangsu Province(BK20210201)the Natural Science Foundation of Henan(Distinguished Young Scholars of Henan Province)(242300421046)the Natural Science Foundation of Sichuan Province(2025ZNSFSC0880)the Guangdong Major Project of Basic and Applied Basic Research(2020B0301030008)the Department of Science and Technology of Shandong province(tsqn202312052,2024HWYQ-005)the Startup Research Fund of Henan Academy of Sciences(20251820001)the Excellent Young Talents Program of Wuhan University of Technology(40122102)the research program of the Wuhan University of Technology(3120625397,2020IB024)the Fundamental Research Funds for the Central Universities(JZ2023HGTB0222,WUT:2022IVA052)the Excellent Scholar Project of Southeast University(Class A)the Big Data Computing Center of Southeast University,National Science and Technology Council,the Ministry of Education(Higher Education Sprout Project NTU-114L104022-1)the Center for Theoretical Sciences of Taiwan,and Vietnam National Foundation for Science and Technology Development(NAFOSTED)(103.01-2023.50)the Research Office of the University of the Witwatersrand and South African Department of Science and Innovation through the SA-CERN programthe self-determined research funds of Central China Normal University from the colleges'basic research and operation of MOE(CCNU24AI003)SJTU Double First Class start-up fund(WF220442604)the Innovation Capability Support Program of Shaanxi(2021KJXX-47)the Slovenian Research Agency under the research core funding No.P1-0035,the research grants J1-3013,N1-0253,CONICET,ANPCyT under project(PICT-2021-00374)Higher Education Sprout Project(NTU-114L104022-1)KIAS Individual Grants(PG086002)at the Korea Institute for Advanced Study,FAPESP(2021/09547-9)the Slovenian Research Agency under the research core funding(P1-0035)research grants J1-3013,N1-0253the bilateral project Proteus PR-12696/Projet 50194VC。
文摘I.EXECUTIVE SUMMARY next-generation,high-intensity electron-positron collider"Higgs factory",such as the Circular Electron-Positron Collider(CEPC),is among the highest priorities for the global high-energy collider physics community.The CEPC can provide unprecedented opportunities for making fundamental discoveries and providing decisive insights in the quest for a"New Standard Model(SM)"of nature's fundamental interactions.The CEPC could:·Identify the origin of matter,especially the mechanism related to the first-order phase transition in the early Universe,which could produce a detectable gravitational wave signal.
