Self-adjoint Wheeler-DeWitt operators, the problem of time, and the wave function of the Universe.

نویسندگان

  • Feinberg
  • Peleg
چکیده

We discuss minisuperspace aspects a non empty Robertson-Walker universe containing scalar matter field. The requirement that the Wheeler-DeWitt (WDW) operator be self adjoint is a key ingredient in constructing the physical Hilbert space and has non-trivial cosmological implications since it is related with the problem of time in quantum cosmology. Namely, if time is parametrized by matter fields we find two types of domains for the self adjoint WDW operator: a non trivial domain is comprised of zero current (Hartle-Hawking type) wave functions and is parametrized by two new parameters, whereas the domain of a self adjoint WDW operator acting on tunneling (Vilenkin type) wave functions is a single ray. On the other hand, if time is parametrized by the scale factor both types of wave functions give rise to non trivial domains for the self adjoint WDW operators, and no new parameters appear in them. PACS numbers: 98.80.Hw, 04.60.Kz, 98.80.Bp, 02.30.Tb ∗ Supported by the Robert A. Welch Foundation and NSF Grant PHY 9009850. Supported by the NSF grants PHY-9105935 and PHY-9315811.

برای دانلود رایگان 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

The Wave Equation in Non-classic Cases: Non-self Adjoint with Non-local and Non-periodic Boundary Conditions

In this paper has been studied the wave equation in some non-classic cases. In the  rst case boundary conditions are non-local and non-periodic. At that case the associated spectral problem is a self-adjoint problem and consequently the eigenvalues are real. But the second case the associated spectral problem is non-self-adjoint and consequently the eigenvalues are complex numbers,in which two ...

متن کامل

Inverse problem for Sturm-Liouville operators with a transmission and parameter dependent boundary conditions

In this manuscript, we consider the inverse problem for non self-adjoint Sturm--Liouville operator $-D^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. We prove by defining a new Hilbert space and using spectral data of a kind, the potential function can be uniquely determined by a set of value of eigenfunctions at an interior point and p...

متن کامل

Error bounds in approximating n-time differentiable functions of self-adjoint operators in Hilbert spaces via a Taylor's type expansion

On utilizing the spectral representation of selfadjoint operators in Hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in Hilbert Spaces via a Taylor's type expansion are given.

متن کامل

Quantization of Closed Mini-superspace Models as Bound States

Wheeler-DeWitt equation is applied to k > 0 Friedmann Robertson Walker metric with various types of matter. It is shown that if the Universe ends in the matter dominated era (e.g., radiation or pressureless gas) with zero cosmological constant, then the resulting Wheeler-DeWitt equation describes a bound state problem. As solutions of a non-degenerate bound state system, the eigen-wave function...

متن کامل

Hilbert space of wormholes.

Wormhole boundary conditions for the Wheeler-DeWitt equation can be derived from the path integral formulation. It is proposed that the wormhole wave function must be square integrable in the maximal analytic extension of minisuperspace. Quantum wormholes can be invested with a Hilbert-space structure, the inner product being naturally induced by the minisuperspace metric, in which the Wheeler-...

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

عنوان ژورنال:
  • Physical review. D, Particles and fields

دوره 52 4  شماره 

صفحات  -

تاریخ انتشار 1995