scholarly journals Bulk Local Operators, Conformal Descendants, and Radial Quantization

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Zhao-Long Wang ◽  
Yi Yan
Keyword(s):  
Field Theory ◽  
Field Equation ◽  
Prior Knowledge ◽  
Free Field ◽  
Finite Energy ◽  
Energy Scale ◽  
Quantization Formalism ◽  
Local Operators

We establish a construction of the bulk local operators in AdS by considering CFT at finite energy scale. Without assuming any prior knowledge about the bulk, the solution to the bulk free field equation automatically appears in the field theory arguments. In the radial quantization formalism, we find a properly regularized version of our initial construction. Possible generalizations beyond pure AdS are also discussed.

scholarly journals THE FREE FIELD REPRESENTATION OF SU(3) CONFORMAL FIELD THEORY

1993 ◽  
Vol 08 (23) ◽  
pp. 4031-4053
Author(s):  
HOVIK D. TOOMASSIAN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Free Field ◽  
Field Representation ◽  
Conformal Field ◽  
Point Correlation

The structure of the free field representation and some four-point correlation functions of the SU(3) conformal field theory are considered.

scholarly journals Variational Solution of the Gross–Neveu Model: Finite N and Renormalization

1997 ◽  
Vol 12 (19) ◽  
pp. 3307-3334 ◽  
Author(s):  
C. Arvanitis ◽  
F. Geniet ◽  
M. Iacomi ◽  
J.-L. Kneur ◽  
A. Neveu
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
General Framework ◽  
Free Field ◽  
Variational Calculation ◽  
Final Point ◽  
Variational Calculations ◽  
Perturbative Renormalization ◽  
Good Agreement ◽  
Gross Neveu Model

We show how to perform systematically improvable variational calculations in the O(2N) Gross–Neveu model for generic N, in such a way that all infinities usually plaguing such calculations are accounted for in a way compatible with the perturbative renormalization group. The final point is a general framework for the calculation of nonperturbative quantities like condensates, masses, etc., in an asymptotically free field theory. For the Gross–Neveu model, the numerical results obtained from a "two-loop" variational calculation are in a very good agreement with exact quantities down to low values of N.

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 Algebraic and differential Rainich conditions for symmetric trace-free tensors of higher rank

2005 ◽  
Vol 461 (2059) ◽  
pp. 2181-2195 ◽  
Author(s):  
Göran Bergqvist ◽  
Paul Lankinen
Keyword(s):  
Field Equation ◽  
Free Field ◽  
Massless Spin ◽  
Complete Set ◽  
Higher Rank ◽  
Necessary And Sufficient ◽  
Differential Condition

We present a study of Rainich-like conditions for symmetric and trace-free tensors T . For arbitrary even rank we find a necessary and sufficient differential condition for a tensor to satisfy the source-free field equation. For rank 4, in a generic case, we combine these conditions with previously obtained algebraic conditions to gain a complete set of algebraic and differential conditions on T for it to be a superenergy tensor of a Weyl candidate tensor, satisfying the Bianchi vacuum equations. By a result of Bell and Szekeres, this implies that in vacuum, generically, T must be the Bel–Robinson tensor of the spacetime. For the rank 3 case, we derive a complete set of necessary algebraic and differential conditions for T to be the superenergy tensor of a massless spin-3/2 field, satisfying the source-free field equation.

Muon-proton deep inelastic scattering and asymptotically free field theory

1977 ◽  
Vol 20 (6) ◽  
pp. 205-209
Author(s):  
K. Watanabe ◽  
K. Ninomiya ◽  
M. Wada
Keyword(s):  
Field Theory ◽  
Inelastic Scattering ◽  
Deep Inelastic Scattering ◽  
Free Field

scholarly journals THERMAL FIELD THEORY IN A WIRE: APPLICATIONS OF THERMAL FIELD THEORY METHODS TO THE PROPAGATION OF PHOTONS IN A ONE-DIMENSIONAL PLASMA

2011 ◽  
Vol 26 (32) ◽  
pp. 5387-5402 ◽  
Author(s):  
JOSÉ F. NIEVES
Keyword(s):  
Field Theory ◽  
Thermal Field Theory ◽  
Thermal Field ◽  
Free Field ◽  
Dynamical Variable ◽  
Effective Field ◽  
Dispersion Relations ◽  
One Dimensional ◽  
Self Energy ◽  
The One

The Thermal Field Theory methods are applied to calculate the dispersion relation of the photon propagating modes in a strictly one-dimensional (1D) ideal plasma. The electrons are treated as a gas of particles that are confined to a 1D tube or wire, but are otherwise free to move, without reference to the electronic wave functions in the coordinates that are transverse to the idealized wire, or relying on any features of the electronic structure. The relevant photon dynamical variable is an effective field in which the two space coordinates that are transverse to the wire are collapsed. The appropriate expression for the photon free-field propagator in such a medium is obtained, the one-loop photon self-energy is calculated and the (longitudinal) dispersion relations are determined and studied in some detail. Analytic formulas for the dispersion relations are given for the case of a degenerate electron gas, and the results differ from the long-wavelength formula that is quoted in the literature for the strictly 1D plasma. The dispersion relations obtained resemble the linear form that is expected in realistic quasi-1D plasma systems for the entire range of the momentum, and which have been observed in this kind of system in recent experiments.

ON p-ADIC FUNCTIONAL INTEGRALS

1988 ◽  
Vol 03 (06) ◽  
pp. 639-643 ◽  
Author(s):  
GIORGIO PARISI
Keyword(s):  
Field Theory ◽  
Quantum Mechanics ◽  
Free Field ◽  
Two Dimensional ◽  
Functional Integrals

In this letter we present a possible form of quantum mechanics in the case where the dynamical variables (or the time) are p-adic numbers. We also present a possible formulation of two-dimensional free field theory on a two-dimensional p-adic space.

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