scholarly journals Asymptotic symmetries of scalar electrodynamics and of the abelian Higgs model in Hamiltonian formulation

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Roberto Tanzi ◽  
Domenico Giulini
Keyword(s):  
Scalar Field ◽  
Gauge Field ◽  
Hamiltonian Formulation ◽  
Scalar Fields ◽  
Higgs Model ◽  
Massless Scalar ◽  
Asymptotic Symmetry ◽  
Abelian Gauge ◽  
Abelian Higgs Model ◽  
Asymptotic Symmetries

Abstract We investigate the asymptotic symmetry group of a scalar field minimally-coupled to an abelian gauge field using the Hamiltonian formulation. This extends previous work by Henneaux and Troessaert on the pure electromagnetic case. We deal with minimally coupled massive and massless scalar fields and find that they behave differently insofar as the latter do not allow for canonically implemented asymptotic boost symmetries. We also consider the abelian Higgs model and show that its asymptotic canonical symmetries reduce to the Poincaré group in an unproblematic fashion.

scholarly journals Asymptotic symmetries of Yang-Mills fields in Hamiltonian formulation

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Roberto Tanzi ◽  
Domenico Giulini
Keyword(s):  
Symplectic Form ◽  
Hamiltonian Formulation ◽  
Hamiltonian Formalism ◽  
Poincaré Group ◽  
Asymptotic Symmetry ◽  
Abelian Gauge ◽  
Poincare Group ◽  
Yang Mills ◽  
Clear Cut ◽  
Asymptotic Symmetries

Abstract We investigate the asymptotic symmetry group of the free SU(N )-Yang-Mills theory using the Hamiltonian formalism. We closely follow the strategy of Henneaux and Troessaert who successfully applied the Hamiltonian formalism to the case of gravity and electrodynamics, thereby deriving the respective asymptotic symmetry groups of these theories from clear-cut first principles. These principles include the minimal assumptions that are necessary to ensure the existence of Hamiltonian structures (phase space, symplectic form, differentiable Hamiltonian) and, in case of Poincaré invariant theories, a canonical action of the Poincaré group. In the first part of the paper we show how these requirements can be met in the non-abelian SU(N )-Yang-Mills case by imposing suitable fall-off and parity conditions on the fields. We observe that these conditions admit neither non-trivial asymptotic symmetries nor non-zero global charges. In the second part of the paper we discuss possible gradual relaxations of these conditions by following the same strategy that Henneaux and Troessaert had employed to remedy a similar situation in the electromagnetic case. Contrary to our expectation and the findings of Henneaux and Troessaert for the abelian case, there seems to be no relaxation that meets the requirements of a Hamiltonian formalism and allows for non-trivial asymptotic symmetries and charges. Non-trivial asymptotic symmetries and charges are only possible if either the Poincaré group fails to act canonically or if the formal expression for the symplectic form diverges, i.e. the form does not exist. This seems to hint at a kind of colour-confinement built into the classical Hamiltonian formulation of non-abelian gauge theories.

On the vacuum stress induced by uniform acceleration or supporting the ether

1977 ◽  
Vol 354 (1676) ◽  
pp. 79-99 ◽  
Keyword(s):  
Scalar Field ◽  
Boundary Conditions ◽  
Neumann Boundary ◽  
Scalar Fields ◽  
Black Body ◽  
Dirichlet Boundary Conditions ◽  
Massless Scalar ◽  
Perfect Conductor ◽  
Infinite Plane ◽  
Uniform Acceleration

The stresses induced in the vacuum by the uniform acceleration of an infinite plane conductor are computed for the massless scalar and electromagnetic fields. Both Dirichlet and Neumann boundary conditions are considered for the scalar field; far from the conductor it is found, independently of the boundary condition, that the vacuum stress is ‘local’ and corresponds to the absence from the vacuum of black body radiation. Approaching the conductor, the energy density in the Dirichlet case is slightly lower than the ‘local’ term, and in the Neumann case slightly higher. At very small distances it again has the same asymptotic form for both scalar fields. For the electromagnetic field the results are similar to those for the scalar field with Dirichlet boundary conditions. Far from the conductor the spectrum is again black-body, though not Planckian. In all cases the acausal nature of ‘ perfect conductor ’ boundary conditions prevents the stress tensor from being finite on the conductor.

Stationary bound states of massless scalar fields around black holes and black hole analogues

2015 ◽  
Vol 24 (09) ◽  
pp. 1542018 ◽  
Author(s):  
Carolina L. Benone ◽  
Luís C. B. Crispino ◽  
Carlos A. R. Herdeiro ◽  
Eugen Radu
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Spatial Distribution ◽  
Scalar Field ◽  
Bound States ◽  
Neumann Boundary ◽  
Mass Term ◽  
Scalar Fields ◽  
Massless Scalar ◽  
Field System

We discuss stationary bound states, a.k.a. clouds, for a massless test scalar field around Kerr black holes (BHs) and spinning acoustic BH analogues. In view of the absence of a mass term, the trapping is achieved via enclosing the BH — scalar field system in a cavity and imposing Dirichlet or Neumann boundary conditions. We discuss the variation of these bounds states with the discrete parameters that label them, as well as their spatial distribution, complementing results in our previous work [C. L. Benone, L. C. B. Crispino, C. Herdeiro and E. Radu, Phys. Rev. D91 (2015) 104038].

DUALITY FOR ANYONS

1989 ◽  
Vol 04 (20) ◽  
pp. 1937-1943 ◽  
Author(s):  
T.H. HANSSON ◽  
A. KARLHEDE
Keyword(s):  
Gauge Field ◽  
Three Dimensional ◽  
Higgs Model ◽  
Duality Transformation ◽  
Abelian Higgs Model ◽  
Topological Excitations ◽  
Fractional Spin ◽  
Conserved Current ◽  
Chern Simons ◽  
Spin And Statistics

We study the Nielsen-Olesen vortices in the three dimensional noncompact Abelian Higgs model with a Chern-Simons term. The vortices are fractionally charged anyons (i.e., particles with fractional spin and statistics). In a certain limit we can express the theory in terms of these topological excitations by performing a duality transformation on the lattice. The result is a topologically conserved current describing the vortices, minimally coupled to a dynamical gauge field with a Chern-Simons term. Spin, statistics and size of the excitations are all preserved under this transformation.

scholarly journals STATIC SPHERICALLY SYMMETRIC SCALAR FIELD SPACETIMES WITH C0 MATCHING

2011 ◽  
Vol 26 (17) ◽  
pp. 1281-1290 ◽  
Author(s):  
SWASTIK BHATTACHARYA ◽  
PANKAJ S. JOSHI
Keyword(s):  
Scalar Field ◽  
Naked Singularity ◽  
Scalar Fields ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Spherically Symmetric ◽  
Curvature Singularity ◽  
Einstein Theory ◽  
Full Class ◽  
Strong Curvature

All the classes of static massless scalar field models currently available in the Einstein theory of gravity necessarily contain a strong curvature naked singularity. We obtain here a family of solutions for static massless scalar fields coupled to gravity, which does not have any strong curvature singularity. This class of models contain a thin shell of singular matter, which has a physical interpretation. The central curvature singularity is, however, avoided which is common to all static massless scalar field spacetime models known so far. Our result thus points out that the full class of solutions in this case may contain non-singular models, which is an intriguing possibility.

scholarly journals The Casimir energy for scalar field with mixed boundary condition

2018 ◽  
Vol 15 (10) ◽  
pp. 1850172 ◽  
Author(s):  
M. A. Valuyan
Keyword(s):  
Scalar Field ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Scalar Fields ◽  
Casimir Energy ◽  
Massless Scalar ◽  
Regularization Technique ◽  
Massive Scalar Field ◽  
Subtraction Scheme ◽  
First Order

In this study, the first-order radiative correction to the Casimir energy for massive and massless scalar fields confined with mixed boundary conditions (BCs) (Dirichlet–Neumann) between two points in [Formula: see text] theory was computed. Two issues in performing the calculations in this work are essential: to renormalize the bare parameters of the problem, a systematic method was employed, allowing all influences from the BCs to be imported in all elements of the renormalization program. This idea yields our counterterms appeared in the renormalization program to be position-dependent. Using the Box Subtraction Scheme (BSS) as a regularization technique is the other noteworthy point in the calculation. In this scheme, by subtracting the vacuum energies of two similar configurations from each other, regularizing divergent expressions and their removal process were significantly facilitated. All the obtained answers for the Casimir energy with the mixed BC were consistent with well-known physical grounds. We also compared the Casimir energy for massive scalar field confined with four types of BCs (Dirichlet, Neumann, mixed of them and Periodic) in [Formula: see text] dimensions with each other, and the sign and magnitude of their values were discussed.

scholarly journals SPHERICALLY SYMMETRIC MASSIVE SCALAR FIELDS IN GENERAL RELATIVITY

2010 ◽  
Vol 25 (07) ◽  
pp. 1429-1438 ◽  
Author(s):  
MOHAMMAD MEHRPOOYA ◽  
D. MOMENI
Keyword(s):  
Scalar Field ◽  
Cosmological Constant ◽  
Scalar Fields ◽  
Matter Field ◽  
Massless Scalar ◽  
Special Choice ◽  
Spherically Symmetric ◽  
Elementary Functions ◽  
Field Equations ◽  
Tidal Forces

First, we review some attempts made to find the exact spherically symmetric solutions to Einstein field equations in the presence of scalar fields. Wyman's solution in both the static and the nonstatic scalar field is discussed, and it is shown why in the case of the nonstatic homogenous matter field the static metric cannot be represented in terms of elementary functions. We mention here that if the space–time is static, according to field equations, there are two options for fixing the scalar field: static (time-independent) and nonstatic (time-dependent). All these solutions are limited to the minimally coupled massless scalar fields and also in the absence of the cosmological constant. Then we show that if we are interested to have homogenous isotropic scalar field matter, we can construct a series solution in terms of the scalar field's mass and cosmological constant. This solution is static and possesses a locally flat case as a special choice of the mass of the scalar field and can be interpreted as an effective vacuum. Therefore, the mass of the scalar field eliminates any locally gravitational effect as tidal forces. Finally, we describe why this system is unstable in the language of dynamical systems.

scholarly journals LATE-TIME TAIL OF A COUPLED SCALAR FIELD IN THE BACKGROUND OF A BLACK HOLE WITH A GLOBAL MONOPOLE

2008 ◽  
Vol 23 (05) ◽  
pp. 359-369 ◽  
Author(s):  
SONGBAI CHEN ◽  
JILIANG JING
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Scalar Fields ◽  
Massless Scalar ◽  
Late Time ◽  
Massless Scalar Field ◽  
Global Monopole ◽  
Massive Scalar Field ◽  
Gravitational Fields ◽  
Field Decay

Using the technique of spectral decomposition, we investigated the late-time tails of massless and massive coupled scalar fields in the background of a black hole with a global monopole. We found that due to the existence of the coupling between the scalar and gravitational fields, the massless scalar field decay faster at timelike infinity i+, and so does the massive one in the intermediate late time. But the asymptotically late-time tail for the massive scalar field is not affected and its decay rate is still t-5/6.

scholarly journals The spectral dimension in 2D CDT gravity coupled to scalar fields

2015 ◽  
Vol 30 (13) ◽  
pp. 1550077 ◽  
Author(s):  
J. Ambjørn ◽  
A. Görlich ◽  
J. Jurkiewicz ◽  
H. Zhang
Keyword(s):  
Scalar Field ◽  
Scalar Fields ◽  
Spectral Dimension ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Two Dimensional ◽  
Imaginary Time ◽  
Causal Dynamical Triangulations ◽  
Pure Gravity ◽  
Dynamical Triangulations

Causal Dynamical Triangulations (CDT) provide a non-perturbative formulation of Quantum Gravity assuming the existence of a global time foliation. In our earlier study we analyzed the effect of including d copies of a massless scalar field in the two-dimensional CDT model with imaginary time. For d > 1 we observed the formation of a "blob", somewhat similar to that observed in four-dimensional CDT without matter. In the two-dimensional case the "blob" has a Hausdorff dimension DH = 3. In this paper, we study the spectral dimension DS of the two-dimensional CDT-universe, both for d = 0 (pure gravity) and d = 4. We show that in both cases the spectral dimension is consistent with DS = 2.

scholarly journals Black holes with regular horizons in Maxwell-scalar gravity

1996 ◽  
Vol 74 (1-2) ◽  
pp. 17-28 ◽  
Author(s):  
Slava G. Turyshev
Keyword(s):  
Black Holes ◽  
Scalar Field ◽  
Scalar Curvature ◽  
Scalar Fields ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Coupling Constant ◽  
Minkowski Space Time ◽  
Special Cases ◽  
Nontrivial Coupling

A class of exact static spherically symmetric solutions of the Einstein–Maxwell gravity coupled to a massless scalar field is obtained in the harmonic coordinates of Minkowski space-time. For each value of the coupling constant a, these solutions are characterized by a set of three parameters, the physical mass μ0, the electric charge Q0 and the scalar-field parameter k. We find that the solutions for both gravitational and electromagnetic fields are not only affected by the scalar field, but also the nontrivial coupling with matter constrains the scalar field itself. In particular, we find that the constant k differs generically from ±1/2, falling into the interval [Formula: see text]. It takes these values only for black holes or in the case when a scalar field [Formula: see text] is totally decoupled from the matter. Our results differ from those previously obtained in that the presence of an arbitrary coupling constant a gives an opportunity to rule out the nonphysical horizons. In one of the special cases, the obtained solution corresponds to a charged dilatonic black hole with only one horizon μ+ and hence to the Kaluza–Klein case. The most remarkable property of this result is that the metric, the scalar curvature, and both the electromagnetic and scalar fields are all regular on this surface. Moreover, while studying the dilaton charge, we found that the inclusion of the scalar field in the theory resulted in a contraction of the horizon. The behavior of the scalar curvature was analysed.

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