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 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 FUNCTIONAL RENORMALIZATION OF NONCOMMUTATIVE SCALAR FIELD THEORY

2011 ◽  
Vol 26 (23) ◽  
pp. 4009-4051 ◽  
Author(s):  
ALESSANDRO SFONDRINI ◽  
TIM A. KOSLOWSKI
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
High Energy ◽  
Flow Equation ◽  
Renormalization Group Equation ◽  
Dual Model ◽  
Group Equation ◽  
Scalar Field Theory ◽  
Covariant Model ◽  
The Matrix

In this paper we apply the Functional Renormalization Group Equation (FRGE) to the noncommutative scalar field theory proposed by Grosse and Wulkenhaar. We derive the flow equation in the matrix representation and discuss the theory space for the self-dual model. The features introduced by the external dimensionful scale provided by the noncommutativity parameter, originally pointed out in R. Gurau and O. J. Rosten, J. High Energy Phys.0907, 064 (2009), are discussed in the FRGE context. Using a technical assumption, but without resorting to any truncation, it is then shown that the theory is asymptotically safe for suitably small values of the ϕ4coupling, recovering the result of M. Disertori et al., Phys. Lett. B649, 95 (2007). Finally, we show how the FRGE can be easily used to compute the one-loop beta-functions of the duality covariant model.

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 POLCHINSKI ERG EQUATION IN O(N) SCALAR FIELD THEORY

2001 ◽  
Vol 16 (11) ◽  
pp. 2065-2070 ◽  
Author(s):  
YURI KUBYSHIN ◽  
RUI NEVES ◽  
ROBERTUS POTTING
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Fixed Points ◽  
Derivative Expansion ◽  
Regular Solutions ◽  
Scalar Field Theory

We investigate the Polchinski ERG equation for d-dimensional O(N) scalar field theory. In the context of the non-pertubative derivative expansion we find families of regular solutions and establish their relation with the physical fixed points of the theory. Special emphasis is given to the limit N=∞ for which many properties can be studied analytically.

scholarly journals Scalar field theory limits of bosonic string amplitudes

2000 ◽  
Vol 579 (1-2) ◽  
pp. 379-410 ◽  
Author(s):  
Alberto Frizzo ◽  
Lorenzo Magnea ◽  
Rodolfo Russo
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Bosonic String ◽  
Scalar Field Theory ◽  
String Amplitudes
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