Dirac Decomposition of Wheeler-DeWitt Equation on the Bianchi Class A Models

نویسنده

  • Hidetomo Yamazaki
چکیده

The Wheeler-DeWitt equation for the Bianchi Class A cosmological models is expressed generally in terms of the second-order differential equation like the Klein-Gordon equation. To obtain the positive-definite probability density, a new method extending the Dirac-Square-Root formalism, which factorizes the Wheeler-DeWitt equation into the first-order differential equation using the Pauli matrices, is investigated. The solutions to the Dirac type equation thus obtained are expressed in terms of two-component spinor form. The probability density defined by the solution is positive-definite and there is a conserved current. The newly found spin-like degree of freedom causes the universe to go through an early quantum stage of evolution with agitated anisotropyoscillation like Zitterbewegung.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Dirac Decomposition of Wheeler-DeWitt Equation in the Bianchi Class A Models

The Wheeler-DeWitt equation in the Bianchi Class A cosmological models is expressed generally in terms of a second-order differential equation, like the Klein-Gordon equation. To obtain a positive definite probability density, a new method is investigated, which extends the Dirac Square Root formalism that factorizes the Wheeler-DeWitt equation into a first-order differential equation using the...

متن کامل

Wheeler - Dewitt Equation with Variable Constants

In this paper we review the basic issues of quantum cosmological models. We explore the Wheeler-DeWitt equation in different contexts but from a dimensional point of view. We end by presenting the Wheeler-DeWitt equation in the case of considering all the constants varying. The quantum potential is obtained and the tunneling probability is studied.

متن کامل

Erratum: (2+1)-dimensional Chern-Simons gravity as a Dirac square root

For simple enough spatial topologies, at least four approaches to (2 + 1)-dimensional quantum gravity have been proposed: Wheeler-DeWitt quantization, canonical quantization in Arnowitt-Deser-Misner (ADM) variables on reduced phase space, Chern-Simons quantization, and quantization in terms of Ashtekar-Rovelli-Smolin loop variables. An important problem is to understand the relationships among ...

متن کامل

Gravitational Entropy and Quantum Cosmology

We investigate the evolution of different measures of “Gravitational Entropy” in Bianchi type I and Lemâitre-Tolman universe models. A new quantity behaving in accordance with the second law of thermodynamics is introduced. We then go on and investigate whether a quantum calculation of initial conditions for the universe based upon the Wheeler-DeWitt equation supports Penrose’s Weyl Curvature C...

متن کامل

0 Thin shell quantization in Weyl spacetime

We study the problem of quantization of thin shells in a Weyl–Dirac theory by deriving a Wheeler–DeWitt equation from the dynamics. Solutions are found which have interpretations in both cosmology and particle physics.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2001