EPR, Bell, GHZ, and Hardy theorems, and quantum mechanics

We review the theorems of Einstein-Podolsky-Rosen (EPR), Bell, Greenberger-Horne-Zeilinger (GHZ), and Hardy, and present arguments supporting the idea that quantum mechanics is a complete, causal, non local, and non separable theory.Comment: 19 pages, 2 figure

The CPT Group of the Dirac Field

Using the standard representation of the Dirac equation we show that, up to signs, there exist only TWO SETS of consistent solutions for the matrices of charge conjugation (C), parity (P), and time reversal (T). In both cases, P^2=-1, and then two succesive applications of the parity transformation to spin 1/2 fields NECESSARILY amounts to a 2\pi rotation. Each of these sets generates a non abelian group of sixteen elements, G_1 and G_2, which are non isomorphic subgroups of the Dirac algebra, which, being a Clifford algebra, gives a geometric nature to the generators, in particular to C. It turns out that G_1 is isomorphic to D_8 x Z_2, where D_8 is the dihedral group of eight elements (the symmetries of the square) and Z_2 is isomorphic to S^0 (the 0-sphere); while G_2 is isomorphic to a certain semidirect product of D_8 and Z_2. Instead, the corresponding quantum operators for C, P, and T generate a UNIQUE group G, which we call THE CPT GROUP OF THE DIRAC FIELD, and which is isomorphic to Q x Z_2, where Q is the quaternion group. This group, however, is compatible only with the second of the above two matrix solutions, namely with G_2, which is then called THE MATRIX CPT GROUP. It is interesting to remark that G_1, G_2, and G are the only non abelian groups of sixteen elements with three generators. Finally, the matrix groups are also given in the Weyl and Majorana representations, suitable for taking the massless limit and for describing self-conjugate fields.Comment: 21 pages, plaintex, some macros of my own, International Journal of Theoretical Physics (to appear

Fibre bundles, connections, general relativity, and Einstein-Cartan theory

We present in the most natural way, that is, in the context of the theory of vector and principal bundles and connections in them, fundamental geometrical concepts related to General Relativity and one of its extensions, the Einstein-Cartan theory.Comment: 60 page

Topology and Collapse

We show that the collapse of the wave function of an entangled state of two spin 1/2 particles or two photons in the singlet state can be geometrically understood as a change of fibre bundles.Comment: 4 pages, no figure

Charge Conjugation in the Galilean Limit

Strictly working in the framework of the nonrelativistic quantum mechanics of a spin 1/2 particle coupled to an external electromagnetic field, we show, by explicit construction, the existence of a charge conjugation operator matrix which defines the corresponding antiparticle wave function and leads to the galilean and gauge invariant Schroedinger-Pauli equation satisfied by it.Comment: 5 page

Einstein-Cartan Theory and Gauge Symmetry

We argue that the non gauge invariant coupling between torsion and the Maxwell or Yang-Mills fields in Einstein-Cartan theory can not be ignored. Arguments based in the existence of normal frames in neighbourhoods, and an approximation to a \delta-function, lead to gauge invariant observables.Comment: Replacement of eq.(8) in v1 by equations (5)-(9) in v

Poincar\'e gauge invariance of general relativity and Einstein-Cartan theory

We present a simple proof of the Poincar\'e gauge invariance of general relativity and Einstein-Cartan theory, in the context of the corresponding bundle of affine frames.Comment: 11 pages, no figure

Leggett inequalities and the completeness of quantum mechanics

We consider the so called Legget inequalities which are deduced from the assumption of general (local or non-local) realism plus the arrow of time preservation. Then, instead of assuming cryto-nonlocal hidden variables, we assume any (local or non-local) realism compatible with the joint and non-joint expected values dictated by quantum mwechaanics. Hence, we prove that this double assumption is not consistent, since the corresponding general Leggett inequalities are violated by quantum mechanics. Thus, realism plus arrow of time preservation and quntum mechanics are not compatible. In other words, quantum mechanics cannot be completed with any (local or non-local) hidden variables, provide we assume the common sense of the arrow of time. The result would deserve to be experimentally tested and we discuss why it is not invalidated by hidden variable theories as the one from Bohm.Comment: 12 pages, articl

Complex ER bridges in EPRB decays

We argue that a great circle in the 7-sphere plays the role of an Einstein-Rosen bridge in Einstein-Podolsky-Rosen-Bohm decays.Comment: 5 pages, 1 figur

Irreducible representations of the CPT groups in QED

We construct the inequivalent irreducible representations (IIR's) of the CPT groups of the Dirac field operator \hat{\psi} and the electromagnetic quantum potential \hat{A}_\mu. The results are valid both for free and interacting (QED) fields. Also, and for the sake of completeness, we construct the IIR's of the CPT group of the Dirac equation.Comment: 15 page