Green's Functions for the One‐Speed Transport Equation in Spherical Geometry

1968 ◽  
Vol 9 (1) ◽  
pp. 81-89 ◽  
Author(s):  
R. C. Erdmann ◽  
C. E. Siewert
Keyword(s):  
Transport Equation ◽  
Green's Functions ◽  
Green’S Functions ◽  
Spherical Geometry ◽  
The One

Thermodynamic Green’s Functions and Spectral Structure

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Spectral Weight ◽  
Statistical Thermodynamic ◽  
Spectral Structure ◽  
Imaginary Time ◽  
Translational Invariance ◽  
The One

Multiparticle thermodynamic Green’s functions, defined in terms of grand canonical ensemble averages of time-ordered products of creation and annihilation operators, are interpreted as tracing the amplitude for time-developing correlated interacting particle motions taking place in the background of a thermal ensemble. Under equilibrium conditions, time-translational invariance permits the one-particle thermal Green’s function to be represented in terms of a single frequency, leading to a Lehmann spectral representation whose frequency poles describe the energy spectrum. This Green’s function has finite values for both t>t′ and t<t′ (unlike retarded Green’s functions), and the two parts G1> and G1< (respectively) obey a simple proportionality relation that facilitates the introduction of a spectral weight function: It is also interpreted in terms of a periodicity/antiperiodicity property of a modified Green’s function in imaginary time capable of a Fourier series representation with imaginary (Matsubara) frequencies. The analytic continuation from imaginary time to real time is discussed, as are related commutator/anticommutator functions, also retarded/advanced Green’s functions, and the spectral weight sum rule is derived. Statistical thermodynamic information is shown to be embedded in physical features of the one- and two-particle thermodynamic Green’s functions.

The one-loop Green’s functions of dimensionally reduced gauge theories

Pramana ◽  
1988 ◽  
Vol 30 (3) ◽  
pp. 173-182 ◽  
Author(s):  
S V Ketov ◽  
Y S Prager
Keyword(s):  
Green's Functions ◽  
Gauge Theories ◽  
Green’S Functions ◽  
The One

scholarly journals RELATING CALCULATIONS AND RENORMALIZATION IN AXIAL AND LORENTZ GAUGES AND GAUGE-INDEPENDENCE

2005 ◽  
Vol 20 (28) ◽  
pp. 6437-6449
Author(s):  
SATISH D. JOGLEKAR
Keyword(s):  
Wave Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Wave Function Renormalization ◽  
Renormalization Procedure ◽  
Point Function ◽  
Starting Point ◽  
Loop Approximation ◽  
The Difference ◽  
The One

We study further the recently developed formalism for the axial gauges toward the comparison of calculations and of the renormalization procedure in the axial and the Lorentz gauges. We do this in the one-loop approximation for the wave function renormalization and the identity of the β-functions in the two gauges. We take as the starting point the relation between the Green's functions in the two gauges obtained earlier. We obtain the relation between the one-loop propagators in the two gauges and locate those diagrams that contribute to the difference between the wave function renormalizations in the two gauges. We further employ this relation between the Green's functions to the case of the 3-point function and prove the identity of the β-functions in the two gauges.

scholarly journals Green’s functions for translation invariant star products

2015 ◽  
Vol 30 (36) ◽  
pp. 1550194
Author(s):  
Fedele Lizzi ◽  
Manolo Rivera ◽  
Patrizia Vitale
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Commutation Relation ◽  
Green's Functions ◽  
Green’S Functions ◽  
Star Product ◽  
Canonical Commutation Relation ◽  
Star Products ◽  
Translation Invariant ◽  
The One

We calculate the Green’s functions for a scalar field theory with quartic interactions for which the fields are multiplied with a generic translation invariant star product. Our analysis involves both non-commutative products, for which there is the canonical commutation relation among coordinates, and nonlocal commutative products. We give explicit expressions for the one-loop corrections to the two- and four-point functions. We find that the phenomenon of ultraviolet/infrared mixing is always a consequence of the presence of non-commuting variables. The commutative part of the product does not have the mixing.

OPERATOR REGULARIZATION AND THE DIVERGENCE OF THE SUPERCURRENT

1987 ◽  
Vol 02 (03) ◽  
pp. 785-796 ◽  
Author(s):  
D. G. C. McKEON ◽  
T. N. SHERRY
Keyword(s):  
Effective Action ◽  
Gauge Invariance ◽  
Green's Functions ◽  
Green’S Functions ◽  
Perturbative Expansion ◽  
Feynman Diagrams ◽  
Spinor Particle ◽  
Yang Mills ◽  
Loop Level ◽  
The One

Operator regularization is introduced as a procedure to compute Green's functions perturbatively. At the one-loop level the effective action is regularized by means of the ζ-function. A perturbative expansion due to Schwinger allows one to compute from the ζ-function one-loop one-particle irreducible Green's functions. By regulating in this way, we do not have to compute Feynman diagrams, we avoid having to introduce a regulating parameter into the initial Lagrangian and we do not encounter any divergent integrals. This procedure is illustrated for N = 1 super Yang-Mills theory in which the one-loop one-particle irreducible Green's function associated with the decay of the supercurrent into a vector and a spinor particle is treated. Gauge invariance is automatically maintained and the usual anomaly in the divergence of the super-current is recovered.

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