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.

One-loop divergences

2021 ◽  
pp. 363-387
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
General Result ◽  
Asymptotic Freedom ◽  
Yukawa Model ◽  
Yang Mills ◽  
Starting Point ◽  
The One ◽  
Mills Field ◽  
Matter Fields

This chapter focuses on one-loop calculations and related issues such as practical renormalization and the derivation of beta functions. The general result for the one-loop divergences from chapter 13 is applied to a sequence of practical calculations. The starting point is the derivation of vacuum divergences of free matter fields. The beta functions in the vacuum sector are calculated. Asymptotic freedom is discussed. In addition, examples of one-loop divergences in interacting theories are elaborated, including the Yang-Mills field coupled to fermions and scalars, and the Yukawa model.

scholarly journals Covariant extrinsic gravity and the geometric origin of dark energy

2015 ◽  
Vol 24 (03) ◽  
pp. 1550027 ◽  
Author(s):  
S. Jalalzadeh ◽  
T. Rostami
Keyword(s):  
Dark Energy ◽  
Density Parameter ◽  
Field Equations ◽  
Yang Mills ◽  
Geometric Origin ◽  
Model Independent ◽  
Bulk Space ◽  
Mills Field ◽  
Matter Fields ◽  
Good Agreement

In this paper, we construct the covariant or model independent induced Einstein–Yang–Mills field equations on a four-dimensional brane embedded isometrically in an D-dimensional bulk space, assuming the matter fields are confined to the brane. Applying this formalism to cosmology, we derive the generalized Friedmann equations. We derive the density parameter of dark energy in terms of width of the brane, normal curvature radii and the number of extra large dimensions. We show that dark energy could actually be the manifestation of the local extrinsic shape of the brane. It is shown that the predictions of this model are in good agreement with observation if we consider an 11-dimensional bulk space.

scholarly journals SYMMETRIC GROUND STATES FOR A STATIONARY RELATIVISTIC MEAN-FIELD MODEL FOR NUCLEONS IN THE NON-RELATIVISTIC LIMIT

2012 ◽  
Vol 24 (10) ◽  
pp. 1250025 ◽  
Author(s):  
MARIA J. ESTEBAN ◽  
SIMONA ROTA NODARI
Keyword(s):  
Nuclear Physics ◽  
Field Model ◽  
Mean Field ◽  
Ground States ◽  
Good Choice ◽  
Coupling Constants ◽  
Mean Field Model ◽  
Relativistic Limit ◽  
Relativistic Mean Field ◽  
The One

In this paper, we consider a model for a nucleon interacting with the ω and σ mesons in the atomic nucleus. The model is relativistic, but we study it in the nuclear physics non-relativistic limit, which is of a very different nature from the one of the atomic physics. Ground states with a given angular momentum are shown to exist for a large class of values for the coupling constants and the mesons' masses. Moreover, we show that, for a good choice of parameters, the very striking shapes of mesonic densities inside and outside the nucleus are well described by the solutions of our model.

scholarly journals PHASE TRANSITION COUPLINGS IN U(1) and SU(N) REGULARIZED GAUGE THEORIES

2001 ◽  
Vol 16 (24) ◽  
pp. 3989-4009 ◽  
Author(s):  
L. V. LAPERASHVILI ◽  
D. A. RYZHIKH ◽  
H. B. NIELSEN
Keyword(s):  
Phase Transition ◽  
Effective Potential ◽  
Gauge Theories ◽  
Planck Scale ◽  
Structure Constant ◽  
Coupling Constants ◽  
Fine Structure Constant ◽  
Multiple Point ◽  
Yang Mills ◽  
Loop Approximation

Using a two-loop approximation for β functions, we have considered the corresponding renormalization group improved effective potential in the dual Abelian Higgs model (DAHM) of scalar monopoles and calculated the phase transition (critical) couplings in U(1) and SU (N) regularized gauge theories. In contrast to our previous result α crit ≈0.17, obtained in the one-loop approximation with the DAHM effective potential (see Ref. 20), the critical value of the electric fine structure constant in the two-loop approximation, calculated in the present paper, is equal to α crit ≈0.208 and coincides with the lattice result for compact QED10: [Formula: see text]. Following the 't Hooft's idea of the "Abelization" of monopole vacuum in the Yang–Mills theories, we have obtained an estimation of the SU (N) triple point coupling constants, which is [Formula: see text]. This relation was used for the description of the Planck scale values of the inverse running constants [Formula: see text] (i= 1, 2, 3 correspond to U(1), SU(2) and SU(3) groups), according to the ideas of the multiple point model.16

INSTANTONS AND SPHALERONS IN SKYRMED WEINBERG–SALAM MODELS AND GRASSMANNIAN MODELS

2000 ◽  
Vol 15 (02) ◽  
pp. 251-264
Author(s):  
F. BRAU ◽  
V. BRIHAYE ◽  
D. H. TCHRAKIAN
Keyword(s):  
Higgs Doublet ◽  
Three Dimensions ◽  
Dimensional System ◽  
One Dimensional ◽  
Yang Mills ◽  
Pure Gauge ◽  
Static Solutions ◽  
The One ◽  
Matter Fields

Several Lagrangians describing the SU(2) Yang–Mills (YM) field interacting with matter are considered, which support both instantons (in four Euclidean dimensions) and sphaleron (in three dimensions, static) solutions. The matter fields are the complex Higgs doublet for the Weinberg–Salam (WS) model, and a (2 × 4) Grassmannian model. These Lagrangians feature Skyrme-like extensions to enable the existence of the instantons, which decay as pure gauge at infinity. For two of these models, we have numerically integrated the one-dimensional system arising from the imposition of radial ansatz.

scholarly journals VORTEX SOLUTION IN (2+1)-DIMENSIONAL PURE YANG–MILLS THEORY AT HIGH TEMPERATURES

1999 ◽  
Vol 14 (27) ◽  
pp. 1909-1916 ◽  
Author(s):  
DMITRI DIAKONOV
Keyword(s):  
High Temperatures ◽  
Higgs Field ◽  
Higgs Potential ◽  
Yang Mills ◽  
Vortex Solution ◽  
The One ◽  
Mills Field ◽  
Stable Vortex

At high temperatures the A0 component of the Yang–Mills field plays the role of the Higgs field, and the one-loop potential V(A0) plays the role of the Higgs potential. We find a new stable vortex solution of the Abrikosov–Nielsen–Olesen type, and discuss its properties and possible implications.

scholarly journals POTENTIAL ENERGY OF YANG–MILLS VORTICES IN THREE AND FOUR DIMENSIONS

1999 ◽  
Vol 14 (25) ◽  
pp. 1725-1732 ◽  
Author(s):  
DMITRI DIAKONOV
Keyword(s):  
Magnetic Flux ◽  
Potential Energy ◽  
Wilson Loop ◽  
Parallel Line ◽  
Vortex Center ◽  
Four Dimensions ◽  
Yang Mills ◽  
Loop Approximation ◽  
The One

We calculate the energy of a Yang–Mills vortex as function of its magnetic flux or as the Wilson loop surrounding the vortex center. The calculation is performed in the one-loop approximation. A parallel line with a potential as function of the Polyakov at nonzero temperatures is drawn. We find that quantized Z(2) vortices are dynamically preferred though vortices with arbitrary fluxes cannot be ruled out.

scholarly journals PATH INTEGRAL QUANTIZATION FOR MASSIVE VECTOR BOSONS

2010 ◽  
Vol 25 (18n19) ◽  
pp. 3603-3619 ◽  
Author(s):  
D. DJUKANOVIC ◽  
J. GEGELIA ◽  
S. SCHERER
Keyword(s):  
Vector Fields ◽  
Consistency Condition ◽  
Canonical Quantization ◽  
Mass Term ◽  
Effective Field ◽  
Coupling Constants ◽  
Massive Vector ◽  
Yang Mills ◽  
Interaction Terms ◽  
Vector Bosons

A parity-conserving and Lorentz-invariant effective field theory of self-interacting massive vector fields is considered. For the interaction terms with dimensionless coupling constants the canonical quantization is performed. It is shown that the self-consistency condition of this system with the second-class constraints in combination with the perturbative renormalizability leads to an SU(2) Yang–Mills theory with an additional mass term.

scholarly journals Phase transitions in models with discrete symmetry

2014 ◽  
Vol 29 (38) ◽  
pp. 1450200
Author(s):  
V. G. Ksenzov ◽  
A. I. Romanov
Keyword(s):  
Phase Transitions ◽  
Scalar Field ◽  
Discrete Symmetry ◽  
Coupling Constants ◽  
Yukawa Interaction ◽  
Massless Fermion ◽  
Loop Approximation ◽  
The One

We investigate a class of models with a massless fermion and a self-interacting scalar field with the Yukawa interaction between these two fields. The models considered are formulated in two and four spacetime dimensions and possess a discrete symmetry. We calculate the chiral condensates which are calculated in the one-loop approximation. We show that the models have phase transitions as a function of the coupling constants.

Gauge Interactions

2021 ◽  
pp. 273-286
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Quantum Electrodynamics ◽  
Integral Method ◽  
Equations Of Motion ◽  
Internal Symmetry ◽  
Symmetry Groups ◽  
Yang Mills ◽  
Path Integral Method ◽  
Popov Ghost ◽  
Mills Field ◽  
Matter Fields

The principle of gauge symmetry is introduced as a consequence of the invariance of the equations of motion under local transformations. We apply it to Abelian, as well as non-Abelian, internal symmetry groups. We derive in this way the Lagrangian of quantum electrodynamics and that of Yang–Mills theories. We quantise the latter using the path integral method and show the need for unphysical Faddeev–Popov ghost fields. We exhibit the geometric properties of the theory by formulating it on a discrete space-time lattice. We show that matter fields live on lattice sites and gauge fields on oriented lattice links. The Yang–Mills field strength is related to the curvature in field space.

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