By Eduard Prugovečki (auth.)
The central cause of this monograph is to offer in a scientific and self-con tained model the elemental tenets, principles and result of a framework for the constant unification of relativity and quantum thought in accordance with a quantum idea of spacetime, and incorporating the fundamental rules of the idea of stochastic areas together with these of Born's reciprocity concept. during this context, via the physicial consistency of the current framework we suggest that the endorsed method of relativistic quantum idea is determined by a constant probabilistic interpretation, that's confirmed to be an immediate extrapolation of the normal interpretation of nonrelativistic quantum mechanics. The important factor here's that we will be able to derive conserved and relativistically convariant chance currents, that are proven to merge into their nonrelativistic opposite numbers within the nonrelativistic restrict, and which even as clarify the actual and mathe matical purposes at the back of the fundamental undeniable fact that no likelihood currents that constantly describe pointlike particle localizability exist in traditional relativistic quantum mechanics. hence, it isn't that we dispense with the concept that oflocality, yet particularly the complex principal thesis is that the classical inspiration of locality in response to aspect like localizability is inconsistent within the realm of relativistic quantum idea, and will get replaced via an idea of quantum locality according to stochastically formulated structures of covariance and relating to the aforementioned currents.
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Additional resources for Stochastic Quantum Mechanics and Quantum Spacetime: A Consistent Unification of Relativity and Quantum Theory Based on Stochastic Spaces
Sample text
In Chapter 4, in the context of quantum spacetime, these optimal resolution generators will turn out to be the nonrelativistic approximations of proper wave functions of ground exciton states of Born's quantum metric operator. Alternatively, in the nonrelativistic harmonic oscillator quark model, they represent the ground state of a quark-antiquark pair constituting a meson (Close, 1979). 25) playa distinctive role, and we shall often use them for specific illustrations of general ideas and arguments.
As a consequence, Qi and pi are self-adjoint operators in the Hilbert spaceL2(r) of square-integrable functions 1/1(q, p), with inner product (1/I111/12)r = jff(q, p) 1/12 (q, p) dq dp. 1), Qi and pi do not commute, but rather satisfy the CCRs: [Qi, Qi] = [pi, Pi] = O. 1) is a special case of the more general form .. a .. QI = P (q, p) + iii api ' a PI = gl (q, p) - iii - . 4) that can be arrived at by gauge transformations of the first kind. 4) will emerge as a very special case of a general realization of (relativistic) CCRs in terms of covariant derivatives, with ji and gi being related to affine connections (cf.
6b), ~q, p (x) is obtained from the configuration space resolution generator Hx) by the operations of translating Hx) in space by the amount q and then boosting it to the 3-velocity p/m. Thus, if we think of Hx) as representing the configuration space proper wave function 10 of an extended test particle of mass m that is used as a microdetector placed at the origin of the laboratory (inertial) frame, then ~q, p (x) is the proper wave function of that test particle after it has been submitted to the kinematical procedures of space translation by q and velocity boost by u = p/m.