arXiv subjects

Chopin Soo

Publications and source records attributed to Chopin Soo.

43 records · Page 3Linked to original sources

arXiv1995

The Standard Model with gravity couplings

In this paper, we examine the coupling of matter fields to gravity within the framework of the Standard Model of particle physics. The coupling is described in terms of Weyl fermions of a definite chirality, and employs only (anti)self-dual or left-handed spin connection fields. It is known from the work of Ashtekar and others that such fields can furnish a complete description of gravity without matter. We show that conditions ensuring the cancellation of perturbative chiral gauge anomalies are not disturbed. We also explore a global anomaly associated with the theory, and argue that its removal requires that the number of fundamental fermions in the theory must be multiples of 16. In addition, we investigate the behavior of the theory under discrete transformations P, C and T; and discuss possible violations of these discrete symmetries, including CPT, in the presence of instantons and the Adler-Bell-Jackiw anomaly.

hep-th↗

arXiv1995

Self-dual variables, positive semi-definite action, and discrete transformations in four-dimensional quantum gravity

A positive semi-definite Euclidean action for arbitrary four-topologies can be constructed by adding appropriate Yang-Mills and topological terms to the Samuel-Jacobson-Smolin action of gravity with (anti)self-dual variables. Moreover, on-shell, the (anti)self-dual sector of the new theory corresponds precisely to all Einstein manifolds in four dimensions. The Lorentzian signature action, and its analytic continuations are also considered. A self-contained discussion is given on the effects of discrete transformations C, P and T on the Samuel-Jacobson-Smolin action, and other proposed actions which utilize self- or anti-self-dual variables as fundamental variables in the description of four-dimensional gravity.

gr-qc↗

arXiv1994

Chiral fermions, Gravity and GUTs

We discuss a global anomaly associated with the coupling of chiral Weyl fermions to gravity. The Standard Model based upon $SU(3){\times}SU(2){\times}{U(1)}$ which has 15 fermions per generation is shown to be inconsistent if all background spin manifolds with signature invariant $τ=8k$ are allowed. Similarly, GUTs based on odd number of Weyl fermions are inconsistent. Consistency can be achieved by adding an extra Weyl fermion which needs to couple only to gravity. For arbitrary $τ$'s, generalized spin structures are needed, and the global anomaly cancellation requires that the net index of the total Dirac operator with spin and internal gauge connections be even. As a result GUTs with fundamental multiplets which contain multiples of 16 Weyls per generation are selected. The simplest consistent GUT is the SO(10) model with a multiplet of 16 Weyls per generation. The combined gravity and internal symmetry gauge group of the theory is then $[Spin(3,1){\times}Spin(10)]/Z_2$. Physical implications of these results are commented on.

hep-th↗

arXiv1994

The Chern-Simons Invariant as the Natural Time Variable for Classical and Quantum Cosmology

We propose that the Chern-Simons invariant of the Ashtekar-Sen connection is the natural internal time coordinate for classical and quantum cosmology. The reasons for this are a number of interesting properties of this functional, which we describe here. 1)It is a function on the gauge and diffeomorphism invariant configuration space, whose gradient is orthogonal to the two physical degrees of freedom, in the metric defined by the Ashtekar formulation of general relativity. 2)The imaginary part of the Chern-Simons form reduces in the limit of small cosmological constant, $Λ$, and solutions close to DeSitter spacetime, to the York extrinsic time coordinate. 3)Small matter-field excitations of the Chern-Simons state satisfy, by virtue of the quantum constraints, a functional Schroedinger equation in which the matter fields evolve on a DeSitter background in the Chern-Simons time. We then n propose this is the natural vacuum state of the theory for $Λ\neq 0$. 4)This time coordinate is periodic on the configuration space of Euclideanized spacetimes, due to the large gauge transformations, which means that physical expectation values for all states in non-perturbative quantum gravity will satisfy the $KMS$ condition, and may then be interpreted as thermal states. 5)Forms for the physical hamiltonians and inner product which support the proposal are suggested, and a new action principle for general relativity, as a geodesic principle on the connection superspace, is found.

gr-qc↗

arXiv1993

Superspace Dynamics and Perturbations Around "Emptiness"

Superspace parametrized by gauge potentials instead of metric three-geometries is discussed in the context of the Ashtekar variables. Among other things, an "internal clock" for the full theory can be identified. Gauge-fixing conditions which lead to the natural geometrical separation of physical from gauge modes are derived with the use of the metric in connection-superspace. A perturbation scheme about an unconventional background which is inaccessible to conventional variables is presented. The resultant expansion retains much of the simplicity of Ashtekar's formulation of General Relativity.

gr-qc↗

arXiv1992

Einstein manifolds in Ashtekar variables: explicit examples

We show that all solutions to the vacuum Einstein field equations may be mapped to instanton configurations of the Ashtekar variables. These solutions are characterized by properties of the moduli space of the instantons. We exhibit explicit forms of these configurations for several well-known solutions, and indicate a systematic way to get new ones. Some interesting examples of these new solutions are described.

hep-th↗

arXiv1992

Brst Cohomology and Invariants of 4D Gravity in Ashtekar Variables

We discuss the BRST cohomologies of the invariants associated with the description of classical and quantum gravity in four dimensions, using the Ashtekar variables. These invariants are constructed from several BRST cohomology sequences. They provide a systematic and clear characterization of non-local observables in general relativity with unbroken diffeomorphism invariance, and could yield further differential invariants for four-manifolds. The theory includes fluctuations of the vierbein fields, but there exits a non-trivial phase which can be expressed in terms of Witten's topological quantum field theory. In this phase, the descent sequences are degenerate, and the corresponding classical solutions can be identified with the conformally self-dual sector of Einstein manifolds. The full theory includes fluctuations which bring the system out of this sector while preserving diffeomorphism invariance.

hep-th↗