Equivalence of one dimensional Lagrangian field theories in the plane I

1985 ◽  
pp. 154-179 ◽  
Author(s):  
Robert B. Gardner ◽  
William F. Shadwick
Keyword(s):  
Field Theories ◽  
One Dimensional

scholarly journals Dimensional Enhancement via Supersymmetry

2011 ◽  
Vol 2011 ◽  
pp. 1-45 ◽  
Author(s):  
M. G. Faux ◽  
K. M. Iga ◽  
G. D. Landweber
Keyword(s):  
Quantum Mechanics ◽  
Representation Theory ◽  
Gauge Invariance ◽  
Extra Dimensions ◽  
Field Theories ◽  
Consistency Test ◽  
One Dimensional ◽  
Supersymmetric Field Theories ◽  
Higher Dimensional ◽  
Supersymmetric Models

We explain how the representation theory associated with supersymmetry in diverse dimensions is encoded within the representation theory of supersymmetry in one time-like dimension. This is enabled by algebraic criteria, derived, exhibited, and utilized in this paper, which indicate which subset of one-dimensional supersymmetric models describes “shadows” of higher-dimensional models. This formalism delineates that minority of one-dimensional supersymmetric models which can “enhance” to accommodate extra dimensions. As a consistency test, we use our formalism to reproduce well-known conclusions about supersymmetric field theories using one-dimensional reasoning exclusively. And we introduce the notion of “phantoms” which usefully accommodate higher-dimensional gauge invariance in the context of shadow multiplets in supersymmetric quantum mechanics.

INTEGRABLE DEFORMATIONS OF THE NONUNITARY MINIMAL CONFORMAL MODEL ℳ3,5

1992 ◽  
Vol 07 (20) ◽  
pp. 5027-5044 ◽  
Author(s):  
G. MUSSARDO
Keyword(s):  
Field Theories ◽  
Conformal Space ◽  
One Dimensional ◽  
Conformal Model ◽  
Integrable Deformation ◽  
Anomalous Dimensions ◽  
Integrable Deformations ◽  
Scaling Region ◽  
The One ◽  
Space Approach

The scaling region of the nonunitary minimal conformal model M3,5 is described by three different integrable massive field theories. We propose the scattering theory for the integrable deformation of M3,5 by the field ψ with anomalous dimensions [Formula: see text]. The spectrum of this theory is confirmed by the Truncation Conformal Space Approach. We also consider the thermodynamics of the one-dimensional quantum system defined by the transfer matrix relative to the deformation of M3,5 by the field φ with anomalous dimensions [Formula: see text]. This deformation drives the original conformal model into a region of the phase diagram where there are plasma oscillations.

THE PRINCIPLE OF MINIMAL SENSITIVITY APPLIED TO A NEW PERTURBATIVE SCHEME IN QUANTUM FIELD THEORY

1989 ◽  
Vol 04 (07) ◽  
pp. 1735-1746 ◽  
Author(s):  
H. F. JONES ◽  
M. MONOYIOS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Dimensional Space ◽  
Exact Result ◽  
Field Theories ◽  
Quantum Field ◽  
One Dimensional ◽  
Perturbative Method ◽  
Improved Accuracy

A recently proposed perturbative method for solving a self-interacting scalar φ4 field theory consists of writing the interaction as gφ2(1+δ) and expanding in powers of δ. The method contains an ambiguity in so far as one could modify the interaction Lagrangian by a factor λ(1−δ). The truncated expansion depends on the unphysical parameter, whereas the exact result does not. We exploit this ambiguity by assigning to λ the value for which the truncated result is stationary, thus minimizing its sensitivity to λ. The technique is applied to field theories in zero-and one-dimensional space-times and gives improved accuracy as compared to fixed λ.

One-dimensional field theories with odd-power self-interactions

1978 ◽  
Vol 18 (4) ◽  
pp. 1095-1101 ◽  
Author(s):  
William C. Fullin
Keyword(s):  
Field Theories ◽  
One Dimensional

scholarly journals Negativity spectrum of one-dimensional conformal field theories

2016 ◽  
Vol 94 (19) ◽  
Author(s):  
Paola Ruggiero ◽  
Vincenzo Alba ◽  
Pasquale Calabrese
Keyword(s):  
Field Theories ◽  
Conformal Field Theories ◽  
One Dimensional ◽  
Conformal Field

scholarly journals Tangent-space methods for uniform matrix product states

2019 ◽  
Author(s):  
Laurens Vanderstraeten ◽  
Jutho Haegeman ◽  
Frank Verstraete
Keyword(s):  
Tangent Space ◽  
Field Theories ◽  
Matrix Product ◽  
Transfer Matrices ◽  
One Dimensional ◽  
Matrix Product States ◽  
Model Hamiltonian ◽  
Different Types ◽  
Space Formalism ◽  
New Applications

In these lecture notes we give a technical overview of tangent-space methods for matrix product states in the thermodynamic limit. We introduce the manifold of uniform matrix product states, show how to compute different types of observables, and discuss the concept of a tangent space. We explain how to variationally optimize ground-state approximations, implement real-time evolution and describe elementary excitations for a given model Hamiltonian. Also, we explain how matrix product states approximate fixed points of one-dimensional transfer matrices. We show how all these methods can be translated to the language of continuous matrix product states for one-dimensional field theories. We conclude with some extensions of the tangent-space formalism and with an outlook to new applications.

QUASI-EXACTLY-SOLVABLE QUANTAL PROBLEMS: ONE-DIMENSIONAL ANALOGUE OF RATIONAL CONFORMAL FIELD THEORIES

1990 ◽  
Vol 05 (04) ◽  
pp. 803-832 ◽  
Author(s):  
A. YU. MOROZOV ◽  
A.M. PERELOMOV ◽  
A.A. ROSLY ◽  
M.A. SHIFMAN ◽  
A.V. TURBINER
Keyword(s):  
Mathematical Formulation ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Solvable Models ◽  
One Dimensional ◽  
Conformal Field ◽  
Exactly Solvable ◽  
Solvable Problems ◽  
Shed Light ◽  
Ordinary Quantum

The class of quasi-exactly-solvable problems in ordinary quantum mechanics discovered recently shows remarkable parallels with rational two-dimensional conformal field theories. This fact suggests that investigation of the quasi-exactly-solvable models may shed light on rational conformal field theories. We discuss a relation between these two theoretical schemes and propose a mathematical formulation for the procedure of constructing quasi-exactly solvable systems. This discussion leads us to a kind of generalization of the Sugawara construction.

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