By John R Klauder

ISBN-10: 9814644625

ISBN-13: 9789814644624

This pioneering booklet addresses the query: Are the normal strategies of canonical quantization absolutely passable, or is there extra to benefit approximately assigning a formal quantum approach to a given classical method? As proven during this publication, the reply to this question is: *The commonplace strategies of canonical quantization will not be the total story!*

This booklet bargains substitute quantization approaches that whole the tale of quantization. The preliminary chapters are designed to provide the recent systems in a transparent and easy demeanour for normal readers. As is important, platforms that convey applicable effects with traditional quantization bring about a similar effects whilst the hot techniques are used for them. although, later chapters research chosen versions that bring about unacceptable effects whilst quantized conventionally. thankfully, those similar versions result in applicable effects while the recent quantization approaches are used.

Readership: Graduate scholars and researchers in quantum mechanics.

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**Additional info for Enhanced Quantization: Particles, Fields and Gravity**

**Sample text**

1 A brief review of selected operator properties Let us pause brieﬂy to recall some properties of operators as they appear in quantum studies. A general operator Y is called Hermitian provided φ|Y |ψ = ψ|Y |φ ∗ when both |φ and |ψ are in the domain of Y , D(Y ). This criterion implies that the Hermitian adjoint of Y , Y † , acts exactly like Y when conﬁned to the domain D(Y ), but that information does not address what is the domain of Y † itself. Speciﬁcally, we can only conclude that D(Y † ) ⊇ D(Y ).

Among the procedures is the choice of “Cartesian phase-space coordinates” singled out to promote to Hermitian operators. This process is complicated because phase space does not have a metric in order to distinguish such coordinates. Even when suitable coordinates are chosen, the quantization may fail in the sense that the classical limit in which Planck’s constant → 0 does not recover the original classical theory. Attention is also paid to singular perturbations for which an interacting quantum theory does not reduce to the free quantum theory as the coupling constant vanishes.

50) is false! Discontinuous perturbations: singular interacting models We now consider alternative interactions that will change the domain of the interacting action functional. 51) where the interaction involves the potential x(t)−4 , in contrast to the principal example of the previous section where the potential was x(t)4 . For the present case, we see that the domain of the interacting model is a fundamentally diﬀerent domain then that of the free model. In particular, for any g > 0, the domain of the interacting model is D−4 (Ag ) = {x : [x˙ 2 + x2 + x−4 ] dt < ∞}, which clearly is markedly diﬀerent from the page 23 January 21, 2015 24 11:50 BC: 9452 - Enhanced Quantization ws-book9x6 Enhanced Quantization: Particles, Fields & Gravity domain D(A0 ) of the free model.

### Enhanced Quantization: Particles, Fields and Gravity by John R Klauder

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