scholarly journals Chiral condensate beyond the one-loop approximation

2017 ◽  
Vol 80 (3) ◽  
pp. 465-468
Author(s):  
V. G. Ksenzov ◽  
A. I. Romanov
Keyword(s):  
Chiral Condensate ◽  
Loop Approximation ◽  
The One

AN IMPROVED ONE-LOOP ANALYSIS OF THE λϕ4 THEORY AT FINITE TEMPERATURE

1987 ◽  
Vol 02 (03) ◽  
pp. 713-728 ◽  
Author(s):  
SWEE-PING CHIA
Keyword(s):  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Zero Temperature ◽  
Coupling Constant ◽  
Loop Analysis ◽  
Temperature Dependent ◽  
Effective Coupling ◽  
Loop Approximation ◽  
The One ◽  
Dependent Mass

The λϕ4 theory with tachyonic mass is analyzed at T ≠ 0 using an improved one-loop approximation in which each of the bare propagators in the one-loop diagram is replaced by a dressed propagator to take into account the higher loop effects. The dressed propagator is characterized by a temperature-dependent mass which is determined by a self-consistent relation. Renomalization is found to be necessarily temperature-dependent. Real effective potential is obtained, giving rise to real effective mass and real coupling constant. For T < Tc, this is achieved by first shifting the ϕ field by its zero-temperature vacuum expectation value. The effective coupling constant is found to exhibit the striking behavior that it approaches a constant nonzero value as T → ∞.

The renormalization group in perturbative quantum gravity

2021 ◽  
pp. 488-493
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Renormalization Group ◽  
Quantum Gravity ◽  
Minimal Subtraction Scheme ◽  
Loop Approximation ◽  
Renormalization Group Equations ◽  
Gauge Fixing ◽  
Perturbative Renormalization ◽  
Fourth Derivative ◽  
Perturbative Quantum ◽  
The One

This is a short chapter summarizing the main results concerning the renormalization group in models of pure quantum gravity, without matter fields. The chapter starts with a critical analysis of non-perturbative renormalization group approaches, such as the asymptotic safety hypothesis. After that, it presents solid one-loop results based on the minimal subtraction scheme in the one-loop approximation. The polynomial models that are briefly reviewed include the on-shell renormalization group in quantum general relativity, and renormalization group equations in fourth-derivative quantum gravity and superrenormalizable models. Special attention is paid to the gauge-fixing dependence of the renormalization group trajectories.

NEUTRINO SELF-ENERGY AND DISPERSION EQUATION IN DENSE MATTER

1996 ◽  
Vol 11 (28) ◽  
pp. 5093-5108 ◽  
Author(s):  
A. PEREZ MARTINEZ ◽  
A. ZEPEDA ◽  
H. PEREZ ROJAS
Keyword(s):  
Energy Gap ◽  
Vector Boson ◽  
Dense Matter ◽  
Self Energy ◽  
Dispersion Equations ◽  
Negative Effective Mass ◽  
Loop Approximation ◽  
Asymmetric Case ◽  
Type Spectrum ◽  
The One

General expressions for the neutrino self-energy and dispersion equations are found in a medium at finite temperature and density. The neutrino self-energy is calculated in the one-loop approximation and using the unitary gauge. The singularities and the absorption mechanisms are discussed. The low momentum (as compared with the vector boson masses) limit of the self-energy is obtained and from it, the dispersion equations for the quasiparticles are found. These solutions exhibit a group velocity smaller than unity which decreases with increasing density and an energy gap leading to a superfluid-type spectrum. In the particle–antiparticle asymmetric case, a negative effective mass is found for neutrinos.

scholarly journals SCALAR EFFECTIVE ACTION IN KREIN SPACE QUANTIZATION

2011 ◽  
Vol 26 (01) ◽  
pp. 31-41 ◽  
Author(s):  
A. REFAEI ◽  
M. V. TAKOOK
Keyword(s):  
Effective Action ◽  
Krein Space ◽  
Physical Interaction ◽  
Running Coupling ◽  
Loop Approximation ◽  
Running Coupling Constant ◽  
Kreĭn Space ◽  
Β Function ◽  
The One ◽  
Krein Space Quantization

In this paper, the λϕ4 scalar field effective action, in the one-loop approximation, is calculated by using the Krein space quantization. We show that the effective action is naturally finite and the singularity does not appear in the theory. The physical interaction mass, the running coupling constant and β-function are then calculated. The effective potential which is calculated in the Krein space quantization is different from the usual Hilbert space calculation, however we show that β-function is the same in the two different methods.

scholarly journals THE TOROID DIPOLE MOMENT OF THE NEUTRINO

1998 ◽  
Vol 13 (30) ◽  
pp. 5257-5277 ◽  
Author(s):  
VLADIMIR M. DUBOVIK ◽  
VALENTIN E. KUZNETSOV
Keyword(s):  
Dipole Moment ◽  
Mass Shell ◽  
Dipole Moments ◽  
Form Factors ◽  
Dispersion Method ◽  
Anapole Moment ◽  
Electromagnetic Interactions ◽  
Loop Approximation ◽  
The Standard Model ◽  
The One

We discuss the third electromagnetic characteristic of the neutrino, i.e. the toroid dipole moment (TDM), in the framework of the Standard Model. The TDM's distinctions from and similarities to an anapole moment are mentioned. The calculations of toroid dipole moments of νe,μ,τ neutrinos have been done by the dispersion method in the one-loop approximation of the SM for the Majorana case and generalized to the Dirac one. We found them to be different from zero in the case of massive as well as massless neutrinos. The behavior of the νe,μ,τ toroid form factors is also presented in the [Formula: see text] range. All external particles are on the mass shell and there are no problems with the physical interpretation of the final result. Some manifestations of the electromagnetic interactions of neutrinos, induced by their toroid moments, are also remarked on.

scholarly journals One-Loop Renormalization of General Noncommutative Yang–Mills Field Model Coupled to Scalar and Spinor Fields

2003 ◽  
Vol 18 (17) ◽  
pp. 3057-3088 ◽  
Author(s):  
I. L. Buchbinder ◽  
V. A. Krykhtin
Keyword(s):  
Field Model ◽  
Coupling Constants ◽  
Noncommutative Field Theory ◽  
Yang Mills ◽  
Interaction Terms ◽  
Spinor Fields ◽  
Loop Approximation ◽  
The One ◽  
Mills Field ◽  
Matter Fields

We study the theory of noncommutative U (N) Yang–Mills field interacting with scalar and spinor fields in the fundamental and the adjoint representations. We include in the action both the terms describing interaction between the gauge and the matter fields and the terms which describe interaction among the matter fields only. Some of these interaction terms have not been considered previously in the context of noncommutative field theory. We find all counterterms for the theory to be finite in the one-loop approximation. It is shown that these counterterms allow to absorb all the divergencies by renormalization of the fields and the coupling constants, so the theory turns out to be multiplicatively renormalizable. In case of 1PI gauge field functions the result may easily be generalized on an arbitrary number of the matter fields. To generalize the results for the other 1PI functions it is necessary for the matter coupling constants to be adapted in the proper way. In some simple cases this generalization for a part of these 1PI functions is considered.

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.

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