Preface

Operator Formulation of Feynman Path Centroid Dynamics for Rotations

“…These momenta can be obtained using Heisenberg’s equations of motion for our position operators along with the generic Hamiltonian for a particle on a ring where is the rotational constant. Another way to generate these operators is to use Dirac’s method for the quantization of constrained systems, with the constrained surface taken to be the circle. , In this case, and are the constrained versions of the usual linear momentum operators.…”

Identity, individuality and indistinguishability in physics and mathematics

“…Noether’s second theorem encodes a generalization of this result to local symmetries, that is, to symmetries defined by an infinite-dimensional Lie group [ 106 – 108 ]. In this case, the existence of local symmetries leads to the existence of relations between the canonical variables of the Hamiltonian formulation called constraints [ 109 – 111 ]. The importance of Noether’s results cannot be overestated since it provides the mathematical foundations of one of the most important achievements of the twentieth century physics, namely the geometrization of the fundamental interactions.…”

“…that they are invariant under gauge transformations). It would always be possible—at least in principle—to project the coordinate-dependent description to a coordinate-independent one in which all the redundant ‘surplus structure’ is removed out (see for instance the notion of reduced phase space in [ 109 , 111 ]). According to the received view, the fact that a coordinate-dependent description might be useful to perform certain calculations should not blind us to the fact that the election of such a description is only a matter of convenience.…”

“…Poincaré invariance rather results from the fact that the underlying space–time is assumed to have a particular symmetry, which is an intrinsic property of this particular space–time [ 53 ]. 16 It is also worth noting that the most sophisticated mathematical formalism for dealing with gauge symmetries—namely, the so-called BRST formalism [ 111 ]—does not proceed by removing the gauge symmetries, but rather by unfolding the higher structure that they convey. Rather than removing the degrees of freedom that are nothing by ‘pure gauge’ (at least according to the received view), the BRST formalism increases the original number of variables by introducing the so-called ghosts , ghosts of ghosts , and so on and so forth.…”

Spacetime Conventionalism Revisited

“…For a rigorous formal overview see Olver (1993). For discussion in the context of gauge theories and quantization see Henneaux and Teitelboim (1992).…”