Causal amplitudes and the Yang-Feldman formalism

1957 ◽  
Vol 53 (4) ◽  
pp. 843-847 ◽  
Author(s):  
J. C. Polkinghorne
Keyword(s):  
Field Theory ◽  
Green’S Functions ◽  
Free Field ◽  
Dispersion Relations ◽  
Matrix Elements ◽  
Field Equations ◽  
Commutation Relations ◽  
The Matrix ◽  
Free Fields ◽  
Set Up

ABSTRACTThe Yang-Feldman formalism vising the Feynman-like Green's functions is set up. The corresponding free fields have non-trivial commutation relations and contain information about the scattering. S-matrix elements are simply the matrix elements of anti-normal products of the field φF′(x). These are evaluated, and they give directly expressions used in the theory of causality and dispersion relations. It is possible to formulate field theory in a form in which the fields obey free field equations and the effects of interaction are contained in their commutation relations.

Vibration spectrum of silver based on metallic interaction

1962 ◽  
Vol 270 (1341) ◽  
pp. 212-218 ◽  
Keyword(s):  
Vibration Spectrum ◽  
Dispersion Relations ◽  
Matrix Elements ◽  
Specific Heats ◽  
The Third ◽  
The Matrix ◽  
Electrostatic Contribution ◽  
Set Up ◽  
Experimental Values ◽  
Secular Determinant

A secular determinant for silver has been set up, in which the ion-ion force constants have been derived from known expressions appearing in the theory of metallic cohesion. The matrix elements have been represented as the sum of three terms. One of these arises from the Coulomb interaction of the ions and has been taken from Kellermann’s work on sodium chloride. The second mainly owes its origin to the exchange forces but includes any effect due to the non-spherical nature of the Fermi surface. It has been calculated from the experimental values of the shear constants after subtracting the electrostatic contribution. The third term is due to the volume forces and has been evaluated by means of two dispersion relations given respectively by de Launay and Bhatia. For this purpose, the bulk modulus for the volume forces has been calculated by Dayal & Tripathi’s method. Vibration frequencies and the specific heats have been calculated separately by the use of both the dispersion relations. Both the theoretical 0-T curves agree with the experimental curve at all temperatures within the accuracy of the calculations.

scholarly journals On the Modular Operator of Mutli-component Regions in Chiral CFT

2021 ◽  
Author(s):  
Stefan Hollands
Keyword(s):  
Field Theory ◽  
Integral Equation ◽  
Hilbert Problem ◽  
Matrix Elements ◽  
New Approach ◽  
Conformal Field ◽  
The Matrix ◽  
Kms Condition ◽  
Modular Operator ◽  
Riemann Hilbert Problem

AbstractWe introduce a new approach to find the Tomita–Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary fields as well as the so-called Kubo–Martin–Schwinger (KMS) condition. These features can be used to transform the problem to a Riemann–Hilbert problem on a covering of the complex plane cut along the regions, which is equivalent to an integral equation for the matrix elements of the modular Hamiltonian. Examples are considered.

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.

scholarly journals A LECTURE ON THE LIOUVILLE VERTEX OPERATORS (REVIEW)

2004 ◽  
Vol 19 (supp02) ◽  
pp. 436-458 ◽  
Author(s):  
J. TESCHNER
Keyword(s):  
Free Field ◽  
Liouville Theory ◽  
Vertex Operators ◽  
Continuous Family ◽  
Matrix Elements ◽  
Crossing Symmetry ◽  
The Matrix

We reconsider the construction of exponential fields in the quantized Liouville theory. It is based on a free-field construction of a continuous family or chiral vertex operators. We derive the fusion and braid relations of the chiral vertex operators. This allows us to simplify the verification of locality and crossing symmetry of the exponential fields considerably. The calculation of the matrix elements of the exponential fields leads to a constructive derivation of the formula proposed by Dorn/Otto and the brothers Zamolodchikov.

ALGEBRAIC APPROACH TO THE PSEUDOHARMONIC OSCILLATOR IN 2D

2002 ◽  
Vol 11 (02) ◽  
pp. 155-160 ◽  
Author(s):  
SHI-HAI DONG ◽  
ZHONG-QI MA
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Algebraic Approach ◽  
Matrix Elements ◽  
Ladder Operators ◽  
Commutation Relations ◽  
The Matrix ◽  
Pseudoharmonic Oscillator ◽  
Analytical Expressions

A realization of the ladder operators for the solutions to the Schrödinger equation with a pseudoharmonic oscillator in 2D is presented. It is shown that those operators satisfy the commutation relations of an SU(1, 1) algebra. Closed analytical expressions are evaluated for the matrix elements of some operators r2 and r∂/∂ r

Mass Radius of the Nucleon

1972 ◽  
Vol 50 (11) ◽  
pp. 1163-1168 ◽  
Author(s):  
M. G. Hare ◽  
G. Papini
Keyword(s):  
Mass Distribution ◽  
Intermediate State ◽  
Energy Momentum Tensor ◽  
Form Factors ◽  
Momentum Tensor ◽  
Dispersion Relations ◽  
Matrix Elements ◽  
State Expansion ◽  
The Matrix ◽  
The Mean

The mean radius of the mass distribution of the nucleon is determined to be [Formula: see text]. The calculation makes use of sidewise, unsubtracted, threshold dominated dispersion relations for the form factors appearing in the matrix elements of the contracted energy–momentum tensor. It uses a π meson–nucleon intermediate state expansion.

RESHETIKHIN-TURAEV AND CRANE-KOHNO-KONTSEVICH 3-MANIFOLD INVARIANTS COINCIDE

1993 ◽  
Vol 02 (01) ◽  
pp. 65-95 ◽  
Author(s):  
SERGEY PIUNIKHIN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Explicit Formula ◽  
Quantum Groups ◽  
Jones Polynomial ◽  
Matrix Elements ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Wznw Model ◽  
The Matrix

The coincidence of two different presentations of Witten 3-manifold invariants is proved. One of them, invented by Reshetikhin and Turaev, is based on the surgery presentation a of 3-manifold and the representation theory of quantum groups; another one, invented by Kohno and Crane and, in slightly different language by Kontsevich, is based on a Heegaard decomposition of a 3-manifold and representations of the Teichmuller group, arising in conformal field theory. The explicit formula for the matrix elements of generators of the Teichmuller group in the space of conformal blocks in the SU(2) k, WZNW-model is given,using the Jones polynomial of certain links.

scholarly journals INTEGRABLE STRUCTURES IN MATRIX MODELS AND PHYSICS OF 2D GRAVITY

1993 ◽  
Vol 08 (22) ◽  
pp. 3831-3882 ◽  
Author(s):  
A. MARSHAKOV
Keyword(s):  
Field Theory ◽  
Matrix Models ◽  
Matrix Model ◽  
2D Gravity ◽  
Model Description ◽  
Physical Role ◽  
Theory Formulation ◽  
The Matrix ◽  
Free Fields ◽  
Effective Description

A review of the appearance of integrable structures in the matrix model description of 2D gravity is presented. Most of the ideas are demonstrated with technically simple but ideologically important examples. Matrix models are considered as a sort of “effective” description of continuum 2D field theory formulation. The main physical role in such a description is played by the Virasoro-W conditions, which can be interpreted as certain unitarity or factorization constraints. Both discrete and continuum (generalized Kontsevich) models are formulated as the solutions to those discrete (continuous) Virasoro-W constraints. Their integrability properties are proved, using mostly the determinant technique highly related to the representation in terms of free fields. The paper also contains some new observations connected with formulation of more-general-than-GKM solutions and deeper understanding of their relation to 2D gravity.

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