Relationship between the usual formulation of a massless scalar field theory and its formulation in terms of a two-form potential

1989 ◽  
Vol 40 (4) ◽  
pp. 1064-1070 ◽  
Author(s):  
W. G. Unruh ◽  
Nathan Weiss
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Scalar Field Theory

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 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 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.

scholarly journals CONVERGENCE OF DERIVATIVE EXPANSIONS IN SCALAR FIELD THEORY

2001 ◽  
Vol 16 (11) ◽  
pp. 2095-2100 ◽  
Author(s):  
TIM R. MORRIS ◽  
JOHN F. TIGHE
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Flow Equation ◽  
Renormalisation Group ◽  
Massless Scalar ◽  
Derivative Expansion ◽  
Scalar Field Theory ◽  
Β Function

The convergence of the derivative expansion of the exact renormalisation group is investigated via the computation of the β function of massless scalar λφ4 theory. The derivative expansion of the Polchinski flow equation converges at one loop for certain fast falling smooth cutoffs. Convergence of the derivative expansion of the Legendre flow equation is trivial at one loop, but also can occur at two loops and in particular converges for an exponential cutoff.

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 CURRENT ALGEBRA AND CONFORMAL FIELD THEORY ON A FIGURE EIGHT

1993 ◽  
Vol 08 (32) ◽  
pp. 5641-5671 ◽  
Author(s):  
A.P. BALACHANDRAN ◽  
G. BIMONTE ◽  
K.S. GUPTA ◽  
G. MARMO ◽  
P. SALOMONSON ◽  
...  
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Current Algebra ◽  
Central Charge ◽  
Conformal Symmetry ◽  
Conformal Anomaly ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Left And Right ◽  
Kirchhoff's Law

We examine the dynamics of a free massless scalar field on a figure eight network. Upon requiring the scalar field to have a well-defined value at the junction of the network, it is seen that the conserved currents of the theory satisfy Kirchhoff’s law, that is that the current flowing into the junction equals the current flowing out. We obtain the corresponding current algebra and show that, unlike on a circle, the left- and right-moving currents on the figure eight do not in general commute in quantum theory. Since a free scalar field theory on a one-dimensional spatial manifold exhibits conformal symmetry, it is natural to ask whether an analogous symmetry can be defined for the figure eight. We find that, unlike in the case of a manifold, the action plus boundary conditions for the network are not invariant under separate conformal transformations associated with left- and right-movers. Instead, the system is, at best, invariant under only a single set of transformations. Its conserved current is also found to satisfy Kirchhoff’s law at the junction. We obtain the associated conserved charges, and show that they generate a Virasoro algebra. Its conformal anomaly (central charge) is computed for special values of the parameters characterizing the network.

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