Thermal Vacuum Polarization Using the Quantum Mechanical Path Integral

1997 ◽  
Vol 12 (30) ◽  
pp. 5387-5396 ◽  
Author(s):  
D. G. C. Mckeon
Keyword(s):  
Path Integral ◽  
Vacuum Polarization ◽  
Thermal Field ◽  
Quantum Mechanical ◽  
Loop Order ◽  
Thermal Vacuum ◽  
One Dimensional ◽  
Loop Expansion ◽  
High Temperature Expansion ◽  
The One

It has been shown how the quantum mechanical path integral can be used to do perturbative calculations in both quantum and thermal field theory to any order of the loop expansion. However, it is not readily apparent how gauge invariance is made manifest in this approach; in this paper we demonstrate how the vacuum polarization in electrodynamics at one-loop order is in fact transverse. We employ the one-dimensional Green's function [Formula: see text] in conjunction with an integration-by-parts procedure akin to that used by Strassler and Bern and Kosower. Surface terms in this approach are all zero. We obtain the high temperature expansion for the vacuum polarization in the static limit.

Vacuum polarization in a background magnetic field in (2 + 1)-dimensional QED

1995 ◽  
Vol 73 (7-8) ◽  
pp. 458-462
Author(s):  
D. G. C. McKeon
Keyword(s):  
Magnetic Field ◽  
Path Integral ◽  
Vacuum Polarization ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Integral Technique ◽  
Background Magnetic Field ◽  
The One

The one-loop vacuum polarization in the presence of a background magnetic field is computed in (2 + 1)-dimensional electrodynamics in which the spinor mass is parity violating. The quantum-mechanical path-integral technique is used to compute matrix elements arising in the context operator regularization.

scholarly journals Path-integral approach to the one-dimensional large-UHubbard model

1992 ◽  
Vol 45 (14) ◽  
pp. 7850-7871 ◽  
Author(s):  
Z. Y. Weng ◽  
D. N. Sheng ◽  
C. S. Ting ◽  
Z. B. Su
Keyword(s):  
Path Integral ◽  
Integral Approach ◽  
One Dimensional ◽  
Path Integral Approach ◽  
The One

scholarly journals THERMAL FIELD THEORY IN A WIRE: APPLICATIONS OF THERMAL FIELD THEORY METHODS TO THE PROPAGATION OF PHOTONS IN A ONE-DIMENSIONAL PLASMA

2011 ◽  
Vol 26 (32) ◽  
pp. 5387-5402 ◽  
Author(s):  
JOSÉ F. NIEVES
Keyword(s):  
Field Theory ◽  
Thermal Field Theory ◽  
Thermal Field ◽  
Free Field ◽  
Dynamical Variable ◽  
Effective Field ◽  
Dispersion Relations ◽  
One Dimensional ◽  
Self Energy ◽  
The One

The Thermal Field Theory methods are applied to calculate the dispersion relation of the photon propagating modes in a strictly one-dimensional (1D) ideal plasma. The electrons are treated as a gas of particles that are confined to a 1D tube or wire, but are otherwise free to move, without reference to the electronic wave functions in the coordinates that are transverse to the idealized wire, or relying on any features of the electronic structure. The relevant photon dynamical variable is an effective field in which the two space coordinates that are transverse to the wire are collapsed. The appropriate expression for the photon free-field propagator in such a medium is obtained, the one-loop photon self-energy is calculated and the (longitudinal) dispersion relations are determined and studied in some detail. Analytic formulas for the dispersion relations are given for the case of a degenerate electron gas, and the results differ from the long-wavelength formula that is quoted in the literature for the strictly 1D plasma. The dispersion relations obtained resemble the linear form that is expected in realistic quasi-1D plasma systems for the entire range of the momentum, and which have been observed in this kind of system in recent experiments.

scholarly journals Comments on open string with ‘massive’ boundary term

2020 ◽  
Vol 476 (2236) ◽  
pp. 20190748
Author(s):  
Arkady A. Tseytlin
Keyword(s):  
Scattering Amplitudes ◽  
Partition Function ◽  
Gauge Field ◽  
Path Integral ◽  
Open String ◽  
One Dimensional ◽  
Conformally Invariant ◽  
Additional Constant ◽  
The One ◽  
Definition Of

We discuss possible definition of open string path integral in the presence of additional boundary couplings corresponding to the presence of masses at the ends of the string. These couplings are not conformally invariant implying that as in a non-critical string case one is to integrate over the one-dimensional metric or reparametrizations of the boundary. We compute the partition function on the disc in the presence of an additional constant gauge field background and comment on the structure of the corresponding scattering amplitudes.

Path integral treatment for the one‐dimensional Natanzon potentials

1993 ◽  
Vol 34 (4) ◽  
pp. 1257-1269 ◽  
Author(s):  
L. Chetouani ◽  
L. Guechi ◽  
A. Lecheheb ◽  
T. F. Hammann
Keyword(s):  
Path Integral ◽  
One Dimensional ◽  
Integral Treatment ◽  
The One

scholarly journals Schrodinger Wave Equation

2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Aaron C.H. Davey
Keyword(s):  
Quantum Mechanics ◽  
Wave Equation ◽  
Quantum Theory ◽  
System Change ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
One Dimensional ◽  
Erwin Schrödinger ◽  
The One ◽  
Over Time

The father of quantum mechanics, Erwin Schrodinger, was one of the most important figures in the development of quantum theory. He is perhaps best known for his contribution of the wave equation, which would later result in his winning of the Nobel Prize for Physics in 1933. The Schrodinger wave equation describes the quantum mechanical behaviour of particles and explores how the Schrodinger wave functions of a system change over time. This project is concerned about exploring the one-dimensional case of the Schrodinger wave equation in a harmonic oscillator system. We will give the solutions, called eigenfunctions, of the equation that satisfy certain conditions. Furthermore, we will show that this happens only for particular values called eigenvalues.

scholarly journals Massive loops in thermal SU(2) Yang–Mills theory: Radiative corrections to the pressure beyond two loops

2017 ◽  
Vol 32 (19n20) ◽  
pp. 1750118 ◽  
Author(s):  
Ingolf Bischer ◽  
Thierry Grandou ◽  
Ralf Hofmann
Keyword(s):  
Low Temperature ◽  
Ground State ◽  
Analytical Continuation ◽  
Radiative Corrections ◽  
Loop Order ◽  
Strong Suppression ◽  
Yang Mills ◽  
Loop Expansion ◽  
The One ◽  
Lower Loop

We address the loop expansion of the pressure in the deconfining phase of SU(2) Yang–Mills thermodynamics. We devise an efficient book-keeping of excluded energy-sign and scattering-channel combinations for the loop four-momenta associated with massive quasiparticles, circulating in (connected) bubble diagrams subject to vertex constraints inherited from the thermal ground state. These radiative corrections modify the one-loop pressure exerted by free thermal quasiparticles. Increasing the loop order in two-particle irreducible (2PI) bubble diagrams, we exemplarily demonstrate a suppressing effect of the vertex constraints on the number of valid combinations. This increasingly strong suppression gave rise to the conjecture in arXiv:hep-th/0609033 that the loop expansion would terminate at a finite order. Albeit the low-temperature dependence of the 2PI 3-loop diagram complies with this behavior, a thorough analysis of the high-temperature situation reveals that the leading power in temperature is thirteen such that this diagram dominates all lower loop orders for sufficiently high temperatures. An all-loop-order resummation of 2PI diagrams with dihedral symmetry is thus required, defining an extremely well-bounded analytical continuation of the low-temperature result.

scholarly journals A COHERENT STATE PATH INTEGRAL FOR ANYONS

1995 ◽  
Vol 10 (12) ◽  
pp. 985-989 ◽  
Author(s):  
J. GRUNDBERG ◽  
T.H. HANSSON
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Coherent States ◽  
Integral Formula ◽  
Harmonic Potential ◽  
One Dimensional ◽  
Change Of Variables ◽  
The One ◽  
State Path

We derive an su (1, 1) coherent state path integral formula for a system of two one-dimensional anyons in a harmonic potential. By a change of variables we transform this integral into a coherent states path integral for a harmonic oscillator with a shifted energy. The shift is the same as the one obtained for anyons by other methods. We justify the procedure by showing that the change of variables corresponds to an su (1, 1) version of the Holstein-Primakoff transformation.

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