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.

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 FIRST LATTICE EVIDENCE FOR A NONTRIVIAL RENORMALIZATION OF THE HIGGS CONDENSATE

1998 ◽  
Vol 13 (29) ◽  
pp. 2361-2367 ◽  
Author(s):  
P. CEA ◽  
L. COSMAI ◽  
M. CONSOLI
Keyword(s):  
Wave Function ◽  
Continuum Limit ◽  
Higgs Mass ◽  
Lattice Simulation ◽  
Wave Function Renormalization ◽  
Renormalization Factor ◽  
Physical Mass ◽  
The Difference ◽  
Ising Limit ◽  
The Continuum

General arguments related to "triviality" predict that, in the broken phase of (λΦ4)4 theory, the condensate <Φ> rescales by a factor Zφ different from the conventional wave function renormalization factor, Z prop . Using a lattice simulation in the Ising limit, we measure Zφ= m2χ from the physical mass and susceptibility and Z prop from the residue of the shifted-field propagator. We find that the two Z's differ, with the difference increasing rapidly as the continuum limit is approached. Since Zφ affects the relation of <Φ> to the Fermi constant, it can sizably affect the present bounds on the Higgs mass.

scholarly journals Analyticity of off-shell Green’s functions in superstring field theory

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ritabrata Bhattacharya ◽  
Ratul Mahanta
Keyword(s):  
Field Theory ◽  
Momentum Space ◽  
Green's Functions ◽  
Green’S Functions ◽  
Lorentz Transformations ◽  
Point Function ◽  
Technical Issue ◽  
Bochner’S Theorem ◽  
Bochner's Theorem

Abstract We consider the off-shell momentum space Green’s functions in closed superstring field theory. Recently in [1], the off-shell Green’s functions — after explicitly removing contributions of massless states — have been shown to be analytic on a domain (to be called the LES domain) in complex external momenta variables. Analyticity of off-shell Green’s functions in local QFTs without massless states in the primitive domain is a well-known result. Using complex Lorentz transformations and Bochner’s theorem allow to extend the LES domain to a larger subset of the primitive domain. For the 2-, 3- and 4-point functions, the full primitive domain is recovered. For the 5-point function, we are not able to obtain the full primitive domain analytically, only a large part of it is recovered. While this problem arises also for higher-point functions, it is expected to be only a technical issue.

Ética e Consciência

2005 ◽  
Vol 13 (25) ◽  
pp. 7-29
Author(s):  
José de Almeida Pereira Arêdes ◽  
Keyword(s):  
Human Life ◽  
Point Problem ◽  
Everyday Experience ◽  
Basic Difference ◽  
Starting Point ◽  
The Difference ◽  
The One

This reflection on ethics has starting point problem: the authenticity. What does one understand by authenticity in human life? Will not authenticity be a beautiful dream, a wandering of philosophers? Our everyday experience fully shows the use of the mask. So, we can ask ourselves: 1) Why should it be otherwise? 2) Could it be otherwise? 3) Which means should one use so that it is otherwise? There seem to exist in nature and history three forces in continuous fight: 1st) the ones that cause the misfortune that now we experience. 2nd) the ones that impel us to refuse the misfortune, that is, the ones that motivate us in search of happiness. The 3rd is, perhaps, our voluntary and conscious contribution to awakening. So our problem is not - what must I do?, but - how must I be? The difference has to do with the basic difference between morality and ethics and has roots in our history. My proposal suggests that it is not enough that we dream or desire to act well to actually act well. It is necessary that we have knowledge (of ourselves and the others) and that we have power, mainly on ourselves. However, our experience shows how fragile is the knowledge that we possess of ourselves (and so refusing the well-known socratic invitation “know thyself") and how fragile is that power, because we are constantly carried along by what we do not want to do (and so we ignore Lao Dzi’s lesson “the one that wins the others is strong; but the one that wins himself is really powerful"). But there is more: though we do what we want, who is it in ourselves that wants what we want? Thus, a practical inquiry on ourselves seems primordial in order to verify which forces act in us and, eventually, to start trying to understand them and to guide them in a more beneficial direction for all the community of living beings of the planet that we inhabit together. Being so, ethics is not only a set of theoretical principles, but over all a set of exercises, guided by a knowledge, that could be able to lead us to a different way of being.

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