scholarly journals On a Riemannian method in quantum theory about curved space-time

1981 ◽  
Vol 31 (11) ◽  
pp. 1249-1255 ◽  
Author(s):  
A. Uhlmann
Keyword(s):  
Quantum Theory ◽  
Space Time ◽  
Curved Space

Strings in curved space-time: Virasoro algebra in the classical and quantum theory

1987 ◽  
Vol 35 (6) ◽  
pp. 1917-1938 ◽  
Author(s):  
Ratindranath Akhoury ◽  
Yasuhiro Okada
Keyword(s):  
Quantum Theory ◽  
Virasoro Algebra ◽  
Space Time ◽  
Curved Space

scholarly journals Schwinger’s approach to Einstein’s gravity and beyond

2014 ◽  
Vol 92 (9) ◽  
pp. 964-967 ◽  
Author(s):  
K.A. Milton
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
20Th Century ◽  
Quantum Electrodynamics ◽  
Particle Physics ◽  
Space Time ◽  
Gravity Theory ◽  
Curved Space ◽  
Theoretical Physicist ◽  
The Subject

J. Schwinger (1918–1994), founder of renormalized quantum electrodynamics, was arguably the leading theoretical physicist of the second half of the 20th century. Thus it is not surprising that he made contributions to gravity theory as well. His students made major impacts on the still uncompleted program of constructing a quantum theory of gravity. Schwinger himself had no doubt of the validity of general relativity, although he preferred a particle physics viewpoint based on gravitons and the associated fields, and not the geometrical picture of curved space–time. This article provides a brief summary of his contributions and attitudes toward the subject of gravity.

scholarly journals Riemannian Geometry Framed as a Generalized Heisenberg Lie Algebra

2019 ◽  
Author(s):  
Joseph E. Johnson
Keyword(s):  
Quantum Theory ◽  
Lie Algebra ◽  
Riemannian Geometry ◽  
Fourier Transforms ◽  
Heisenberg Algebra ◽  
Space Time ◽  
Einstein Equations ◽  
Curved Space ◽  
Mathematical Generalization ◽  
Structure Constants

The Heisenberg Lie algebra (HA) plays an important role in mathematics with Fourier transforms, as well as for the foundations of quantum theory where it expresses the operators of space-time, X, and their commutation rules with the momentum operators, D, that execute infinitesimal translations in X. Yet it is known that space-time is curved and thus the D operators must interfere thus giving “structure constants” that vary with location which suggests a mathematical generalization of the concept of a Lie algebra to allow for “structure constants” that are functions of X. We here investigate the mathematics of such a “generalized Heisenberg algebra” (GHA) which has “structure constants” that are functions of X and thus are in the enveloping algebra rather than constants. As expected, the Jacobi identity no longer holds globally but only in small regions of space-time where the [D, X] commutator can be considered locally constant and thus where one has a true Lie algebra. We show that one is able to reframe Riemannian geometry in this GHA. As an example, it is then shown that one can express the Einstein equations of general relativity as commutation rules. If one requires that the GHA commutator reduces to the HA of quantum theory in the limit of no curvature, then there are observable effects for quantum theory in this curved space time.

Topology knots and hierarchy problem

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Quantum Gravity ◽  
Dimensional Space ◽  
Space Time ◽  
Elementary Particles ◽  
Hierarchy Problem ◽  
Topological Quantum ◽  
Dimensional Space Time ◽  
New Formula

Many approaches to quantum gravity consider the revision of the space-time geometry and the structure of elementary particles. One of the main candidates is string theory. It is possible that this theory will be able to describe the problem of hierarchy, provided that there is an appropriate Calabi-Yau geometry. In this paper we will proceed from the traditional view on the structure of elementary particles in the usual four-dimensional space-time. The only condition is that quarks and leptons should have a common emerging structure. When a new formula for the mass of the hierarchy is obtained, this structure arises from topological quantum theory and a suitable choice of dimensional units.

Path integrals and the solution of the Schwinger model in curved space-time

1986 ◽  
Vol 33 (8) ◽  
pp. 2262-2266 ◽  
Author(s):  
J. Barcelos-Neto ◽  
Ashok Das
Keyword(s):  
Path Integrals ◽  
Space Time ◽  
Curved Space ◽  
Schwinger Model

Asymptotic behavior of the effective potential of composite fields in a curved space-time

1988 ◽  
Vol 31 (2) ◽  
pp. 163-167
Author(s):  
I. L. Bukhbinder ◽  
S. D. Odintsov
Keyword(s):  
Asymptotic Behavior ◽  
Effective Potential ◽  
Space Time ◽  
Curved Space

A kinetic model of dipole particles in curved space-time

1980 ◽  
Vol 12 (12) ◽  
pp. 1035-1041 ◽  
Author(s):  
J. Tafel
Keyword(s):  
Kinetic Model ◽  
Space Time ◽  
Curved Space

scholarly journals ε-EXPANSION IN QUANTUM FIELD THEORY IN CURVED SPACE–TIME

1998 ◽  
Vol 13 (16) ◽  
pp. 2857-2874
Author(s):  
IVER H. BREVIK ◽  
HERNÁN OCAMPO ◽  
SERGEI ODINTSOV
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Space Time ◽  
Quantum Field ◽  
Curved Space ◽  
Njl Model ◽  
Effective Lagrangian ◽  
Special Solutions ◽  
Curvature Approximation ◽  
Symmetric Phase

We discuss ε-expansion in curved space–time for asymptotically free and asymptotically nonfree theories. The existence of stable and unstable fixed points is investigated for fϕ4 theory and SU(2) gauge theory. It is shown that ε-expansion maybe compatible with aysmptotic freedom on special solutions of the RG equations in a special ase (supersymmetric theory). Using ε-expansion RG technique, the effective Lagrangian for covariantly constant gauge SU(2) field and effective potential for gauged NJL model are found in (4-ε)-dimensional curved space (in linear curvature approximation). The curvature-induced phase transitions from symmetric phase to asymmetric phase (chromomagnetic vacuum and chiral symmetry broken phase, respectively) are discussed for the above two models.

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