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
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
A classical field theory for a Schrodinger equation with a non-Hermitian Hamiltonian describing a particle with position-dependent mass has been recently advanced by Nobre and Rego-Monteiro(NR)[Phys.Rev.A 88(2013)0321...A classical field theory for a Schrodinger equation with a non-Hermitian Hamiltonian describing a particle with position-dependent mass has been recently advanced by Nobre and Rego-Monteiro(NR)[Phys.Rev.A 88(2013)032105].This field theory is based on a variational principle involving the wavefunction Ψ(x,t) and an auxiliary fieldΦ{x,t).It is here shown that the relation between the dynamics of the auxiliary field Φ(x,t) and that of the original wavefunction Ψ(x,t) is deeper than suggested by the NR approach.Indeed,we formulate a variational principle for the aforementioned Schrodinger equation which is based solely on the wavefunction Ψ(x,t).A continuity equation for an appropriately defined probability density,and the concomitant preservation of the norm,follows from this variational principle via Noether's theorem.Moreover,the norm-conservation law obtained by NR is reinterpreted as tie preservation of the inner product between pairs of solutions of the variable mass Schrodinger equation.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
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 generalize several well known quantum equations to a Tsallis’ q-scenario, and provide a quantum version of some classical fields associated with them in the recent literature. We refer to the q-Schro¨dinger, ...We generalize several well known quantum equations to a Tsallis’ q-scenario, and provide a quantum version of some classical fields associated with them in the recent literature. We refer to the q-Schro¨dinger, q-KleinGordon, q-Dirac, and q-Proca equations advanced in, respectively, Phys. Rev. Lett. 106, 140601(2011), EPL 118,61004(2017) and references therein. We also introduce here equations corresponding to q-Yang-Mills fields, both in the Abelian and non-Abelian instances. We show how to define the q-quantum field theories corresponding to the above equations, introduce the pertinent actions, and obtain equations of motion via the minimum action principle.These q-fields are meaningful at very high energies(Te V scale) for q = 1.15, high energies(Ge V scale) for q = 1.001,and low energies(Me V scale) for q =1.000001 [Nucl. Phys. A 955(2016) 16 and references therein].(See the ALICE experiment at the LHC). Surprisingly enough, these q-fields are simultaneously q-exponential functions of the usual linear fields’ logarithms.展开更多
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A classical field theory for a Schrodinger equation with a non-Hermitian Hamiltonian describing a particle with position-dependent mass has been recently advanced by Nobre and Rego-Monteiro(NR)[Phys.Rev.A 88(2013)032105].This field theory is based on a variational principle involving the wavefunction Ψ(x,t) and an auxiliary fieldΦ{x,t).It is here shown that the relation between the dynamics of the auxiliary field Φ(x,t) and that of the original wavefunction Ψ(x,t) is deeper than suggested by the NR approach.Indeed,we formulate a variational principle for the aforementioned Schrodinger equation which is based solely on the wavefunction Ψ(x,t).A continuity equation for an appropriately defined probability density,and the concomitant preservation of the norm,follows from this variational principle via Noether's theorem.Moreover,the norm-conservation law obtained by NR is reinterpreted as tie preservation of the inner product between pairs of solutions of the variable mass Schrodinger equation.
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.
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 generalize several well known quantum equations to a Tsallis’ q-scenario, and provide a quantum version of some classical fields associated with them in the recent literature. We refer to the q-Schro¨dinger, q-KleinGordon, q-Dirac, and q-Proca equations advanced in, respectively, Phys. Rev. Lett. 106, 140601(2011), EPL 118,61004(2017) and references therein. We also introduce here equations corresponding to q-Yang-Mills fields, both in the Abelian and non-Abelian instances. We show how to define the q-quantum field theories corresponding to the above equations, introduce the pertinent actions, and obtain equations of motion via the minimum action principle.These q-fields are meaningful at very high energies(Te V scale) for q = 1.15, high energies(Ge V scale) for q = 1.001,and low energies(Me V scale) for q =1.000001 [Nucl. Phys. A 955(2016) 16 and references therein].(See the ALICE experiment at the LHC). Surprisingly enough, these q-fields are simultaneously q-exponential functions of the usual linear fields’ logarithms.
