Gauge Interactions

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.

Covariant extrinsic gravity and the geometric origin of dark energy

International Journal of Modern Physics D ◽

10.1142/s0218271815500273 ◽

2015 ◽

Vol 24 (03) ◽

pp. 1550027 ◽

Cited By ~ 6

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.

PATH-INTEGRAL FORMULATION OF CASIMIR EFFECTS IN SUPERSYMMETRIC QUANTUM ELECTRODYNAMICS

Modern Physics Letters A ◽

10.1142/s0217732399001097 ◽

1999 ◽

Vol 14 (16) ◽

pp. 1033-1042 ◽

Cited By ~ 4

Author(s):

HIROYUKI ABE ◽

JUNYA HASHIDA ◽

TAIZO MUTA ◽

AGUS PURWANTO

Keyword(s):

Boundary Condition ◽

Path Integral ◽

Quantum Electrodynamics ◽

Integral Method ◽

Mass Term ◽

Casimir Energy ◽

Mass Dependence ◽

Path Integral Formulation ◽

Suitable Boundary Condition ◽

Path Integral Method

The path-integral method of calculating the Casimir energy between two parallel conducting plates is developed within the framework of supersymmetric quantum electrodynamics at vanishing temperature as well as at finite temperature. The choice of the suitable boundary condition for the photino on the plates is argued and the physically acceptable condition is adopted which eventually breaks the supersymmetry. The photino mass term is introduced in the Lagrangian and the photino mass dependence of the Casimir energy and pressure is fully investigated.

ON THE β-FUNCTION AND CONFORMAL ANOMALY OF NONCOMMUTATIVE QED WITH ADJOINT MATTER FIELDS

10.1142/s0217751x0301231x ◽

2003 ◽

Vol 18 (15) ◽

pp. 2591-2607 ◽

Cited By ~ 3

Author(s):

NÉDA SADOOGHI ◽

MOJTABA MOHAMMADI

Keyword(s):

Gauge Theory ◽

Integral Method ◽

Degrees Of Freedom ◽

Adjoint Representation ◽

Conformal Anomaly ◽

Loop Order ◽

Path Integral Method ◽

Β Function ◽

The One ◽

In the first part of this work, a perturbative analysis up to one-loop order is carried out to determine the one-loop β-function of noncommutative U(1) gauge theory with matter fields in the adjoint representation. In the second part, the conformal anomaly of the same theory is calculated using Fujikawa's path integral method. The value of the one-loop β-function calculated in both methods coincides. As it turns out, noncommutative QED with matter fields in the adjoint representation is asymptotically free for the number of flavor degrees of freedom Nf < 3.

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

10.1142/s0217751x03014241 ◽

2003 ◽

Vol 18 (17) ◽

pp. 3057-3088 ◽

Cited By ~ 2

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 ◽

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

Introduction to Quantum Field Theory with Applications to Quantum Gravity ◽

10.1093/oso/9780198838319.003.0014 ◽

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 ◽

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.

Observables of the Generalized 2D Yang–Mills Theories on Arbitrary Surfaces: A Path Integral Approach

Modern Physics Letters A ◽

10.1142/s0217732397002338 ◽

1997 ◽

Vol 12 (30) ◽

pp. 2265-2270 ◽

Cited By ~ 11

Author(s):

M. Khorrami ◽

M. Alimohammadi

Keyword(s):

Partition Function ◽

Path Integral ◽

Integral Method ◽

Integral Approach ◽

Generating Functional ◽

Yang Mills ◽

Path Integral Approach ◽

Nonorientable Surfaces ◽

Path Integral Method ◽

Field Strengths

Using the path integral method, we calculate the partition function and the generating functional (of the field strengths) of the generalized 2-D Yang–Mills theories in the Schwinger–Fock gauge. Our calculation is done for arbitrary 2-D orientable, and also nonorientable surfaces.

Equations of motion of a non-Abelian charged spin particle in a Yang-Mills field

Physical Review D ◽

10.1103/physrevd.26.1979 ◽

1982 ◽

Vol 26 (8) ◽

pp. 1979-1982 ◽

Cited By ~ 3

Author(s):

S. Ragusa

Keyword(s):

Equations Of Motion ◽

Yang Mills ◽

Spin Particle ◽

Mills Field

GENERALIZED RICCI FLOW AND SUPERGRAVITY VACUUM SOLUTIONS

10.1142/s0217751x10048238 ◽

2010 ◽

Vol 25 (12) ◽

pp. 2535-2549 ◽

Cited By ~ 4

Author(s):

SEN HU ◽

ZHI HU ◽

RUORAN ZHANG

Keyword(s):

Modulus Space ◽

Dirac Operator ◽

Flux Compactifications ◽

Ricci Flow ◽

Integral Method ◽

Equations Of Motion ◽

Type Ii ◽

Flow Equations ◽

Path Integral Method ◽

Vacuum Solutions

We first give a proof that the supersymmetric configurations satisfy the equations of motion for type II supergravity. In flux compactifications, the string vacua preserving N = 2 supersymmetry are the twisted generalized Calabi–Yau manifold. The modulus space of the string vacua can be constructed. We discuss the generalized Dirac operator which adds a torsional term to the ordinary Dirac operator and compute its index by the path integral method. Via the variation of the action of supergravity one can introduce the generalized Ricci flow equations. We consider deforming the manifold with the generalized Ricci flow. Finally, we consider the linear stability of the fixed points of the generalized Ricci flow.

n-Point Functions of 2d Yang–Mills Theories on Riemann Surfaces

10.1142/s0217751x97001237 ◽

1997 ◽

Vol 12 (11) ◽

pp. 1959-1965 ◽

Cited By ~ 13

Author(s):

M. Alimohammadi ◽

M. Khorrami

Keyword(s):

Field Theory ◽

Riemann Surfaces ◽

Integral Method ◽

Free Field ◽

Green Functions ◽

Two Dimensional ◽

Gauge Invariant ◽

Gauge Groups ◽

Yang Mills ◽

Path Integral Method

Using the simple path integral method we calculate the n-point functions of field strength of Yang–Mills theories on arbitrary two-dimensional Riemann surfaces. In U(1) case we show that the correlators consist of two parts, a free and an x-independent part. In the case of non-Abelian semisimple compact gauge groups we find the nongauge-invariant correlators in Schwinger–Fock gauge and show that it is also divided to a free and an almost x-independent part. We also find the gauge-invariant Green functions and show that they correspond to a free field theory.