On "Electromagnetic Potential Vectors and Spontaneous Symmetry Breaking"

The appearance of terms, which are analogous to ones required for symmetry breaking, in Lagrangian of Ref. [1] is shown to be caused by gauge invariance of quantum electrodynamics (QED) and by inaccuracy of the cited author in the choice of canonical variables. These terms do not have physical significance within modern quantum electrodynamics. PACS: 03.50.De, 04.20.Cv, 04.20.Fy, 11.10.Ef.Comment: 4 pages, LaTeX file, no figures. This version is to be published in "Relativity, Gravitation, Cosmology: Beyond Foundations" (Nova Science Pubs., Hauppauge, NY, USA, 2018). Ed. V. V. Dvoeglazo

Self/Anti-Self Charge Conjugate States for j=1/2 and j=1

We briefly review recent achievements in the theory of neutral particles (the Majorana-McLennan-Case-Ahluwalia construct for self/anti-self charge conjugate states for j=1/2 and j=1 cases). Among new results we present a theoretical construct in which a fermion and an antifermion have the same intrinsic parity; discuss phase transformations and find relations between the Majorana-like field operator $\nu$, given by Ahluwalia, and the Dirac field operator. Also we give explicit forms of the $j=1$ ``spinors" in the Majorana representation.Comment: ReVTEX file, 11p

Photon-Notoph Equations

In the sixties Ogievetskii and Polubarinov proposed the concept of a notoph, whose helicity properties are complementary to those of a photon. We analyze the theory of antisymmetric tensor fields in the view of the normalization problem. The obtained result is that it is possible to describe both photon and notoph degrees of freedom on the basis of the modified Bargmann-Wigner formalism for the symmetric second-rank spinor. Physical consequences are discussed.Comment: ReVTeX file, 10pp., no figure

A Note on the Neutrino Theory of Light

In this small note we ask several questions which are relevant to the construction of the self-consistent neutrino theory of light. The previous confusions in such attempts are explained in the more detailed publication.Comment: ReVTeX file, no figures, 6p

A Note on the Majorana Theory for j=1/2j=1/2 and j=1j=1 Particle States

The wave equations for self/anti-self conjugate Majorana-McLennan-Case $j=1/2$ and $j=1$ spinors, proposed by Ahluwalia, are re-written to covariant form. The connection with the Foldy-Nigam-Bargmann-Wightman-Wigner (FNBWW) type quantum field theory is discussed.Comment: REVTEX file. 8pp. No figures. Contribution at the XVIII Oaxtepec Symp. on Nuclear Physics. January 4-7, 199

Is the Space-Time Non-Commutativity Simply Non-Commutativity of Derivatives?

Recently, some problems have been found in the definition of the partial derivative in the case of the presence of both explicit and implicit functional dependencies in the classical analysis. In this talk we investigate the influence of this observation on the quantum mechanics and classical/quantum field theory. Surprisingly, some commutators of the coordinate-dependent operators are not equal to zero. Therefore, we try to provide mathematical foundations to the modern non-commutative theories. We also indicate possible applications in the Dirac-like theories.Comment: 8pp., no figures. Talk presented at the 8th International Conference on Squeezed States and Uncertainty Relations (ICSSUR'2003), Puebla, Pue., M\'exico, June 9-13, 200

The Bargmann-Wigner Formalism for Spin 2

We proceed to derive equations for the symmetric tensor of the second rank on the basis of the Bargmann-Wigner formalism in a straightforward way. The symmetric multispinor of the fourth rank is used. It is constructed out of the Dirac 4-spinors. Due to serious problems with the interpretation of the results obtained on using the standard procedure we generalize it and obtain the spin-2 relativistic equations, which are consistent with the previous one. The importance of the 4-vector field (and its gauge part) is pointed out.Comment: ReVTeX file, 6p

On the existence of additional solutions for equations in the (1/2,0)⊕(0,1/2)(1/2,0)\oplus (0,1/2) representation space

We analyze dispersion relations of the equations recently proposed by Ahluwalia for describing neutrino. Equations for type-II spinors are deduced on the basis of the Wigner rules for left- and right- 2-spinors and the Ryder-Burgard relation. It is shown that equations contain acausal solutions which are similar to those of the Dirac-like second-order equation. The latter is obtained in a similar way, provided that we do not apply to any constraints in the process of its deriving.Comment: ReVTeX file, 5pp., no figure

Notoph-Graviton-Photon Coupling

In the sixties Ogievetskii and Polubarinov proposed the concept of a notoph, whose helicity properties are complementary to those of a photon. Later, Kalb and Ramond (and others) developed this theoretical concept. And, at the present times it is widely accepted. We analyze the quantum theory of antisymmetric tensor fields with taking into account mass dimensions of notoph and photon. It appears to be possible to describe both photon and notoph degrees of freedom on the basis of the modified Bargmann-Wigner formalism for the symmetric second-rank spinor. Next, we proceed to derive equations for the symmetric tensor of the second rank on the basis of the Bargmann-Wigner formalism in a straightforward way. The symmetric multispinor of the fourth rank is used. It is constructed out of the Dirac 4-spinors. Due to serious problems with the interpretation of the results obtained on using the standard procedure we generalize it and obtain the spin-2 relativistic equations, which are consistent with the general relativity. The importance of the 4-vector field (and its gauge part) is pointed out. Thus, we present the full theory which contains photon, notoph (the Kalb-Ramond field) and the graviton. The relations of this theory with the higher spin theories are established. In fact, we deduced the gravitational field equations from relativistic quantum mechanics. We estimate possible interactions, fermion-notoph, graviton-notoph, photon-notoph. PACS number: 03.65.Pm, 04.50.-h, 11.30.CpComment: 21 pp. Invited paper for "Frontiers in Physics", http://www.frontiersin.org/ . Also presented at the QTS-8, El Colegio Nacional, Mexico city, Aug. 5-9, 2013. Small revisions for the presentations at the FFP-14, Marseille, France, July 2014 and "What comes beyond the Standard Model?" Bled, Slovenia, July 2014. To appear in the Proceeding

The Barut Second-Order Equation, Dynamical Invariants and Interactions

The second-order equation in the (1/2,0)+(0,1/2) representation of the Lorentz group has been proposed by A. Barut in the beginning of the 70s. It permits to explain the mass splitting of leptons e,mu,tau. Recently, the interest has grown to this model (see, for instance, the papers by S. Kruglov and J. P. Vigier et al.). We continue the research deriving the equation from the first principles, finding the dynamical invariants for this model, investigating the influence of the potential interactions.Comment: 7 pages, no figures, a talk given at the VI Mexican School on Gravitation and Mathematical Physics "Approaches to Quantum Gravity", Nov. 21-27, 2004, Playa del Carmen, QR, Mexic