Linearly Rising Trajectories in an Infinite-Component Field Theory

1970 ◽  
Vol 2 (4) ◽  
pp. 793-801 ◽  
Author(s):  
Alan Chodos ◽  
Richard W. Haymaker
Keyword(s):  
Field Theory ◽  
Component Field ◽  
Infinite Component

Lagrangian approach to infinite component field theory

1968 ◽  
Vol 8 (3) ◽  
pp. 573-590
Author(s):  
H. Watanabe ◽  
S. Kamefuchi
Keyword(s):  
Field Theory ◽  
Lagrangian Approach ◽  
Component Field ◽  
Infinite Component

scholarly journals STRINGS AND MEMBRANES FROM EINSTEIN GRAVITY, MATRIX MODELS AND W∞ GAUGE THEORIES AS PATHS TO QUANTUM GRAVITY

2008 ◽  
Vol 23 (24) ◽  
pp. 3901-3945
Author(s):  
CARLOS CASTRO
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Order Approximation ◽  
Quantum Hall ◽  
Einstein Gravity ◽  
Irreducible Representations ◽  
Large N ◽  
Conformal Spin ◽  
Infinite Component ◽  
2D And 3D

It is shown how w∞, w1+∞ gauge field theory actions in 2D emerge directly from 4D gravity. Strings and membranes actions in 2D and 3D originate as well from 4D Einstein gravity after recurring to the nonlinear connection formalism of Lagrange–Finsler and Hamilton–Cartan spaces. Quantum gravity in 3D can be described by a W∞ matrix model in D = 1 that can be solved exactly via the collective field theory method. We describe why a quantization of 4D gravity could be attained via a 2D quantum W∞ gauge theory coupled to an infinite-component scalar-multiplet. A proof that noncritical W∞ (super)strings are devoid of BRST anomalies in dimensions D = 27(D = 11), respectively, follows and which coincide with the critical (super)membrane dimensions D = 27(D = 11). We establish the correspondence between the states associated with the quasifinite highest weights irreducible representations of W∞, [Formula: see text] algebras and the quantum states of the continuous Toda molecule. Schrödinger-like quantum mechanics wave functional equations are derived and solutions are found in the zeroth-order approximation. Since higher-conformal spin W∞ symmetries are very relevant in the study of 2DW∞ gravity, the quantum Hall effect, large N QCD, strings, membranes, … it is warranted to explore further the interplay among all these theories.

scholarly journals SCHIZOSYMMETRY: A NEW PARADIGM FOR SUPERFIELD EXPANSIONS

1994 ◽  
Vol 09 (25) ◽  
pp. 2305-2313 ◽  
Author(s):  
R. DELBOURGO ◽  
P.D. JARVIS ◽  
ROLAND C. WARNER
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Model Building ◽  
Space Time ◽  
Unified Model ◽  
Quantum Field ◽  
New Paradigm ◽  
Field Transformation ◽  
Component Field ◽  
Symmetry Generators

A new principle of ‘schizosymmetry’ is proposed for interpreting superfield expansions over Grassmann parameters in quantum field theory. Symmetry generators T phys , determining component field transformation properties, are allowed to depend on the grading via T phys =Tℙ e +T′ℙ o , where ℙ e and ℙ o are the projections onto even and odd components in the Grassmann coordinates, respectively, and T and T′ correspond to different representations. Examples are given for both internal and space-time schizosymmetry. In the latter case, superfield expansions have components with both integer and half-integer spin. A program for the Lagrangian realization of schizosymmetry, including unified model building, is outlined.

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