scholarly journals MAPPING A MASSLESS SCALAR FIELD THEORY ON A YANG–MILLS THEORY: CLASSICAL CASE

2009 ◽  
Vol 24 (30) ◽  
pp. 2425-2432 ◽  
Author(s):  
MARCO FRASCA
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Field Equations ◽  
Scalar Field Theory ◽  
Classical Level ◽  
Gradient Expansion ◽  
Yang Mills ◽  
Mills Field

We analyze a recent proposal to map a massless scalar field theory onto a Yang–Mills theory at classical level. It is seen that this mapping exists at a perturbative level when the expansion is a gradient expansion. In this limit the theories share the spectrum, at the leading order, that is the one of a harmonic oscillator. Gradient expansion is exploited maintaining Lorentz covariance by introducing a fifth coordinate and turning the theory to Euclidean space. These expansions give common solutions to scalar and Yang–Mills field equations that are so proved to exist by construction, confirming that the selected components of the Yang–Mills field are indeed an extremum of the corresponding action functional.

scholarly journals Non-linear composition and infinite conformal symmetry of topologically non-trivial solutions in $$(3+1)$$-dimensional Yang–Mills theory

2021 ◽  
Vol 81 (11) ◽  
Author(s):  
Fabrizio Canfora
Keyword(s):  
Scalar Field ◽  
Charge Density ◽  
Topological Charge ◽  
Conformal Symmetry ◽  
Analytic Solutions ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Field Equations ◽  
Yang Mills ◽  
Non Linear

AbstractAn infinite-dimensional family of analytic solutions in pure SU(2) Yang–Mills theory at finite density in $$(3+1)$$ ( 3 + 1 ) dimensions is constructed. It is labelled by two integeres (p and q) as well as by a two-dimensional free massless scalar field. The gauge field depends on all the 4 coordinates (to keep alive the topological charge) but in such a way to reduce the (3+1)-dimensional Yang–Mills field equations to the field equation of a 2D free massless scalar field. For each p and q, both the on-shell action and the energy-density reduce to the action and Hamiltonian of the corresponding 2D CFT. The topological charge density associated to the non-Abelian Chern–Simons current is non-zero. It is possible to define a non-linear composition within this family as if these configurations were “Lego blocks”. The non-linear effects of Yang–Mills theory manifest themselves since the topological charge density of the composition of two solutions is not the sum of the charge densities of the components. This leads to an upper bound on the amplitudes in order for the topological charge density to be well-defined. This suggests that if the temperature and/or the energy is/are high enough, the topological density of these configurations is not well-defined anymore. Semiclassically, one can show that (depending on whether the topological charge is even or odd) some of the operators appearing in the 2D CFT should be quantized as Fermions (despite the Bosonic nature of the classical field).

scholarly journals All-loop order critical exponents for massless scalar field theory with Lorentz violation in the BPHZ method

2016 ◽  
Vol 30 (03) ◽  
pp. 1550259 ◽  
Author(s):  
Paulo R. S. Carvalho
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Critical Exponents ◽  
Lorentz Violation ◽  
Mathematical Explanation ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Loop Order ◽  
Scalar Field Theory ◽  
Loop Level

We compute analytically the all-loop level critical exponents for a massless thermal Lorentz-violating (LV) O(N) self-interacting [Formula: see text] scalar field theory. For that, we evaluate, firstly explicitly up to next-to-leading loop order and later in a proof by induction up to any loop level, the respective [Formula: see text]-function and anomalous dimensions in a theory renormalized in the massless BPHZ method, where a reduced set of Feynman diagrams to be calculated is needed. We investigate the effect of the Lorentz violation in the outcome for the critical exponents and present the corresponding mathematical explanation and physical interpretation.

scholarly journals Massless scalar field theory in a quantized spacetime

1995 ◽  
Vol 12 (3) ◽  
pp. 637-650 ◽  
Author(s):  
J C Breckenridge ◽  
V Elias ◽  
T G Steele
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Scalar Field Theory

scholarly journals ON LAGRANGE STRUCTURE OF UNFOLDED FIELD THEORY

2011 ◽  
Vol 26 (07n08) ◽  
pp. 1347-1362 ◽  
Author(s):  
D. S. KAPARULIN ◽  
S. L. LYAKHOVICH ◽  
A. A. SHARAPOV
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Local Field ◽  
Infinite Number ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Field Equations ◽  
D’Alembert Equation ◽  
Local Field Theory ◽  
Scalar Field Equations

Any local field theory can be equivalently reformulated in the so-called unfolded form. General unfolded equations are non-Lagrangian even though the original theory is Lagrangian. Making use of the unfolded massless scalar field equations as a basic example, the concept of Lagrange anchor is applied to perform a consistent path-integral quantization of unfolded dynamics. It is shown that the unfolded representation for the canonical Lagrange anchor of the d'Alembert equation inevitably involves an infinite number of space–time derivatives.

scholarly journals COLLAPSING SCALAR FIELD WITH KINEMATIC SELF-SIMILARITY OF THE SECOND KIND IN (2+1) GRAVITY

2005 ◽  
Vol 14 (06) ◽  
pp. 1049-1061 ◽  
Author(s):  
R. CHAN ◽  
M. F. A. DA SILVA ◽  
J. F. VILLAS DA ROCHA ◽  
ANZHONG WANG
Keyword(s):  
Black Holes ◽  
Scalar Field ◽  
Gravitational Collapse ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Field Equations ◽  
Self Similarity ◽  
Global Properties ◽  
Scalar Field Equations

All the (2+1)-dimensional circularly symmetric solutions with kinematic self-similarity of the second kind to the Einstein-massless-scalar field equations are found and their local and global properties are studied. It is found that some of them represent gravitational collapse of a massless scalar field, in which black holes are always formed.

scholarly journals Wormholes in Wyman's solution

2014 ◽  
Vol 23 (11) ◽  
pp. 1450086 ◽  
Author(s):  
J. B. Formiga ◽  
T. S. Almeida
Keyword(s):  
Scalar Field ◽  
General Solution ◽  
Detailed Analysis ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Human Beings ◽  
Einstein Field Equations ◽  
Field Equations

The most general solution of the Einstein field equations coupled with a massless scalar field is known as Wyman's solution. This solution is also present in the Brans–Dicke theory and, due to its importance, it has been studied in detail by many authors. However, this solutions has not been studied from the perspective of a possible wormhole. In this paper, we perform a detailed analysis of this issue. It turns out that there is a wormhole. Although we prove that the so-called throat cannot be traversed by human beings, it can be traversed by particles and bodies that can last long enough.

scholarly journals QUANTUM NOETHER'S THEOREM AND CONFORMAL FIELD THEORY: A STUDY OF SOME MODELS

1999 ◽  
Vol 11 (05) ◽  
pp. 519-532 ◽  
Author(s):  
SEBASTIANO CARPI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Scaling Limit ◽  
Momentum Tensor ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Quantum Field ◽  
Time Dimension ◽  
Complex Scalar

We study the problem of recovering Wightman conserved currents from the canonical local implementations of symmetries which can be constructed in the algebraic framework of quantum field theory, in the limit in which the region of localization shrinks to a point. We show that, in a class of models of conformal quantum field theory in space-time dimension 1+1, which includes the free massless scalar field and the SU(N) chiral current algebras, the energy-momentum tensor can be recovered. Moreover we show that the scaling limit of the canonical local implementation of SO(2) in the free complex scalar field is zero, a manifestation of the fact that, in this last case, the associated Wightman current does not exist.

Sign in / Sign up

Export Citation Format

Share Document