scholarly journals ON COVARIANT DERIVATIVES AND GAUGE INVARIANCE IN THE PROPER TIME FORMALISM FOR STRING THEORY

1996 ◽  
Vol 11 (04) ◽  
pp. 317-329 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Gauge Field ◽  
Gauge Invariance ◽  
Covariant Derivative ◽  
Proper Time ◽  
Gauge Fields ◽  
Minimal Coupling ◽  
Covariant Derivatives ◽  
Time Formalism ◽  
Free Level ◽  
Higher Spin

It is shown that the idea of “minimal” coupling to gauge fields can be conveniently implemented in the proper time formalism by identifying the equivalent of a “covariant derivative”. This captures some of the geometric notion of the gauge field as a connection. The proper time equation is also generalized so that the gauge invariances associated with higher spin massive modes can be made manifest, at the free level, using loop variables. Some explicit examples are worked out illustrating these ideas.

scholarly journals THE PROPER TIME FORMALISM, GAUGE INVARIANCE AND THE EFFECTS OF A FINITE WORLD SHEET CUTOFF IN STRING THEORY

1995 ◽  
Vol 10 (31) ◽  
pp. 4501-4519 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Gauge Transformation ◽  
Gauge Invariance ◽  
Proper Time ◽  
World Sheet ◽  
Massive Mode ◽  
Yang Mills ◽  
Previous Discussion ◽  
Time Formalism ◽  
Klein Gordon ◽  
Type Interaction

We discuss the issue of going off-shell in the proper time formalism. This is done by keeping a finite world sheet cutoff. We construct one example of an off-shell covariant Klein-Gordon type interaction. For a suitable choice of the gauge transformation of the scalar field, gauge invariance is maintained off-mass-shell. However, at the second order in the gauge field interaction, one finds that [U(1)] gauge invariance is violated due to the finite cutoff. Interestingly, we find, to the lowest order, that by adding a massive mode with appropriate gauge transformation laws to the sigma model background, we can restore gauge invariance. The gauge transformation law is found to be consistent, to the order calculated, with what one expects from the interacting equation of motion of the massive field. We also extend some previous discussion on applying the proper time formalism for propagating gauge particles, to the interacting (i.e. Yang-Mills) case.

scholarly journals CONFORMAL INVARIANT INTERACTION OF A SCALAR FIELD WITH HIGHER SPIN FIELD IN AdSD

2010 ◽  
Vol 25 (16) ◽  
pp. 1333-1348 ◽  
Author(s):  
RUBEN MANVELYAN ◽  
KARAPET MKRTCHYAN
Keyword(s):  
Scalar Field ◽  
Gauge Field ◽  
Explicit Form ◽  
Gauge Fields ◽  
Conformal Invariant ◽  
Gauge Invariant ◽  
Exact Agreement ◽  
Higher Spin ◽  
Spin Fields ◽  
Invariant Interaction

The explicit form of linearized gauge invariant interactions of scalar and general higher even spin fields in the AdSD space is obtained. In the case of general spin-ℓ a generalized "Weyl" transformation is proposed and the corresponding "Weyl" invariant action is constructed. In both cases the invariant actions of the interacting higher even spin gauge field and the scalar field include the whole tower of invariant actions for couplings of the same scalar with all gauge fields of smaller even spin. For the particular value of ℓ = 4, all results are in exact agreement with Ref. 1.

scholarly journals On the equivalence among stress tensors in a gauge-fluid system

2017 ◽  
Vol 32 (36) ◽  
pp. 1750210 ◽  
Author(s):  
Arpan Krishna Mitra ◽  
Rabin Banerjee ◽  
Subir Ghosh
Keyword(s):  
Gauge Field ◽  
Essential Role ◽  
Fluid Model ◽  
Gauge Fields ◽  
Fluid System ◽  
Relativistic Field ◽  
First Order ◽  
Time Formalism ◽  
Dynamical Nature ◽  
Time Transformations

In this paper, we bring out the subtleties involved in the study of a first-order relativistic field theory with auxiliary field variables playing an essential role. In particular, we discuss the nonisentropic Eulerian (or Hamiltonian) fluid model. Interactions are introduced by coupling the fluid to a dynamical Maxwell (U(1)) gauge field. This dynamical nature of the gauge field is crucial in showing the equivalence, on the physical subspace, of the stress tensor derived from two definitions, i.e. the canonical (Noether) one and the symmetric one. In the conventional equal-time formalism, we have shown that the generators of the space–time transformations obtained from these two definitions agree modulo the Gauss constraint. This equivalence in the physical sector has been achieved only because of the dynamical nature of the gauge fields. Subsequently, we have explicitly demonstrated the validity of the Schwinger condition. A detailed analysis of the model in lightcone formalism has also been done where several interesting features are revealed.

Spinor gauge field in the spinor space–time formalism

1978 ◽  
Vol 56 (3) ◽  
pp. 395-398
Author(s):  
Nguyen Thi Hong
Keyword(s):  
Gauge Field ◽  
Equations Of Motion ◽  
Space Time ◽  
Gauge Fields ◽  
Spinor Representation ◽  
Field Equations ◽  
Gauge Transformations ◽  
Spinor Space ◽  
Time Formalism ◽  
Representation Of Space

In our previous work a method of realizing the bilinear spinor representation of space–time has been suggested, in the language of the spinor coordinates the field equations of motion have been considered. In this work, proceeding from these equations of motion, we consider the spinor gauge fields appearing in the local gauge transformations in the spinor space–time.

scholarly journals Nilpotent symmetries as a mechanism for Grand Unification

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Lars Andersson ◽  
András László ◽  
Błażej Ruba
Keyword(s):  
Gauge Field ◽  
Scalar Product ◽  
Local Symmetry ◽  
Matter Field ◽  
Gauge Fields ◽  
Spacetime Symmetries ◽  
Invariant Scalar ◽  
Spacetime Manifold ◽  
Local Symmetries ◽  
Dilatation Group

Abstract In the classic Coleman-Mandula no-go theorem which prohibits the unification of internal and spacetime symmetries, the assumption of the existence of a positive definite invariant scalar product on the Lie algebra of the internal group is essential. If one instead allows the scalar product to be positive semi-definite, this opens new possibilities for unification of gauge and spacetime symmetries. It follows from theorems on the structure of Lie algebras, that in the case of unified symmetries, the degenerate directions of the positive semi-definite invariant scalar product have to correspond to local symmetries with nilpotent generators. In this paper we construct a workable minimal toy model making use of this mechanism: it admits unified local symmetries having a compact (U(1)) component, a Lorentz (SL(2, ℂ)) component, and a nilpotent component gluing these together. The construction is such that the full unified symmetry group acts locally and faithfully on the matter field sector, whereas the gauge fields which would correspond to the nilpotent generators can be transformed out from the theory, leaving gauge fields only with compact charges. It is shown that already the ordinary Dirac equation admits an extremely simple prototype example for the above gauge field elimination mechanism: it has a local symmetry with corresponding eliminable gauge field, related to the dilatation group. The outlined symmetry unification mechanism can be used to by-pass the Coleman-Mandula and related no-go theorems in a way that is fundamentally different from supersymmetry. In particular, the mechanism avoids invocation of super-coordinates or extra dimensions for the underlying spacetime manifold.

scholarly journals Bulk interactions and boundary dual of higher-spin-charged particles

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Adrian David ◽  
Yasha Neiman
Keyword(s):  
Relative Velocity ◽  
Black Hole Solution ◽  
Vector Model ◽  
Boundary Theory ◽  
Gauge Fields ◽  
Leading Order ◽  
Gravitational Forces ◽  
Penrose Transform ◽  
Higher Spin ◽  
Non Locality

Abstract We consider higher-spin gravity in (Euclidean) AdS4, dual to a free vector model on the 3d boundary. In the bulk theory, we study the linearized version of the Didenko-Vasiliev black hole solution: a particle that couples to the gauge fields of all spins through a BPS-like pattern of charges. We study the interaction between two such particles at leading order. The sum over spins cancels the UV divergences that occur when the two particles are brought close together, for (almost) any value of the relative velocity. This is a higher-spin enhancement of supergravity’s famous feature, the cancellation of the electric and gravitational forces between two BPS particles at rest. In the holographic context, we point out that these “Didenko-Vasiliev particles” are just the bulk duals of bilocal operators in the boundary theory. For this identification, we use the Penrose transform between bulk fields and twistor functions, together with its holographic dual that relates twistor functions to boundary sources. In the resulting picture, the interaction between two Didenko-Vasiliev particles is just a geodesic Witten diagram that calculates the correlator of two boundary bilocals. We speculate on implications for a possible reformulation of the bulk theory, and for its non-locality issues.

scholarly journals Kerr-Newman stress-tensor from minimal coupling

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Ming-Zhi Chung ◽  
Yu-tin Huang ◽  
Jung-Wook Kim
Keyword(s):  
Form Factor ◽  
Stress Tensor ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Minimal Coupling ◽  
Massive Spin ◽  
Stress Energy ◽  
Newman Black Hole ◽  
Higher Spin ◽  
The One

Abstract In this paper, we demonstrate that at leading order in post Minkowskian (PM) expansion, the stress-energy tensor of Kerr-Newman black hole can be recovered to all orders in spin from three sets of minimal coupling: the electric and gravitational minimal coupling for higher-spin particles, and the “minimal coupling” for massive spin-2 decay. These couplings are uniquely defined from kinematic consideration alone. This is shown by extracting the classical piece of the one-loop stress-energy tensor form factor, which we provide a basis that is valid to all orders in spin. The 1 PM stress tensor, and the metric in the harmonic gauge, is then recovered from the classical spin limit of the form factor.

scholarly journals Vertex Corrections in Gauge Theories for Two-dimensional Condensed Matter Systems

1998 ◽  
Vol 12 (16n17) ◽  
pp. 1673-1692 ◽  
Author(s):  
Peter Kopietz
Keyword(s):  
Gauge Field ◽  
Condensed Matter ◽  
Finite Energy ◽  
Energy Scale ◽  
Gauge Fields ◽  
Logarithmic Correction ◽  
Two Dimensional ◽  
Numerical Constant ◽  
Self Energy ◽  
Vertex Corrections

We calculate the self-energy of two-dimensional fermions that are coupled to transverse gauge fields, taking two-loop corrections into account. Given a bare gauge field propagator that diverges for small momentum transfers q as 1/qη, 1<η≤ 2, the fermionic self-energy without vertex corrections vanishes for small frequencies ω as Σ(ω)∝ ωγ with γ=2/(1+η)<1. We show that inclusion of the leading radiative correction to the fermion-gauge field vertex leads to Σ(ω)∝ωγ [1-aη ln (ω0/ω)], where aη is a positive numerical constant and ω0 is some finite energy scale. The negative logarithmic correction is consistent with the scenario that higher order vertex corrections push the exponent γ to larger values.

scholarly journals Nonperturbative one-loop effective action for QED with Yukawa couplings

2018 ◽  
Vol 33 (27) ◽  
pp. 1850157 ◽  
Author(s):  
Theodore N. Jacobson ◽  
Tonnis ter Veldhuis
Keyword(s):  
Effective Action ◽  
Proper Time ◽  
Background Field ◽  
Field Approximation ◽  
Chiral Anomaly ◽  
Dirac Fermion ◽  
Yukawa Couplings ◽  
Time Formalism ◽  
The One ◽  
The Relationship

We derive the one-loop effective action for scalar, pseudoscalar, and electromagnetic fields coupled to a Dirac fermion in an extension of QED with Yukawa couplings. Using the Schwinger proper-time formalism and zeta-function regularization, we calculate the full nonperturbative effective action to one loop in the constant background field approximation. Our result is nonperturbative in the external fields, and goes beyond existing results in the literature which treat only the first nontrivial order involving the pseudoscalar. The result has an even and odd part, which are related to the modulus and phase of the fermion functional determinant. The even contribution to the effective action involves the modulus of the effective Yukawa couplings and is invariant under global chiral transformations while the odd contribution is proportional to the angle between the scalar and pseudoscalar couplings. In different limits the effective action reduces either to the Euler–Heisenberg effective action or the Coleman–Weinberg potential. We also comment on the relationship between the odd part of the effective action and the chiral anomaly in QED.

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