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Mathematical Physics Seminar

Unimodular Bohmian Geometrodynamics

Maaneli Derakhshani - Rutgers University 

Location:  Hill 705
Date & time: Thursday, 12 September 2019 at 2:00PM - 3:00PM

ABSTRACT:  Quantum geometrodynamics (QGD), the version of quantum gravity based on the Wheeler-DeWitt equation, is perhaps the most well-known approach to canonical quantization of general relativity theory. It is known that QGD suffers from three interrelated problems [1, 2, 3]: 1) the Problem of Time, 2) the Quantum Measurement Problem, and 3) the Hilbert Space Problem. As a response to these problems, some researchers have combined geometrodynamics with the Bohmian approach to quantum theory [2, 3], and it has been argued that Bohmian geometrodynamics (BGD) can overcome some or all of these problems.

As another response to the above problems, I will discuss current work combining "unimodular" geometrodynamics [4] with the Bohmian approach to quantum theory. I will argue that:

(i) unimodular Bohmian geometrodynamics (UBGD) is free of problems 1) and 2), and probably can overcome problem 3);

(ii) UBGD makes it possible to describe sub-systems of the quantum-gravitational and matter degrees of freedom via 'conditional wave functionals' and their corresponding equations of motion; and

(iii) the Bohmian semiclassical approximation technique discussed in [5] can be formally extended to UBGD, thereby making possible the formulation of 'semiclassical UBGD'. Time permitting, I will then compare and contrast UBGD with BGD.

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