[5] **viXra:1306.0236 [pdf]**
*replaced on 2014-07-10 08:46:29*

**Authors:** Leonardo Pedro

**Comments:** 31 Pages.

The formulation of quantum mechanics with a complex Hilbert space
is equivalent to a formulation with a real Hilbert space and particular density matrix and
observables. We study the real representations of the Poincare group, motivated by the fact
that the localization of complex unitary representations of the Poincare group is incompatible
with causality, Poincare covariance and energy positivity.
We review the map from the complex to the real irreducible representations—finite-
dimensional or unitary—of a Lie group on a Hilbert space. Then we show that all the
finite-dimensional real representations of the identity component of the Lorentz group are
also representations of the parity, in contrast with many complex representations.
We show that any localizable unitary representation of the Poincare group, compatible
with Poincare covariance, verifies: 1) it is self-conjugate (regardless it is real or complex); 2)
it is a direct sum of irreducible representations which are massive or massless with discrete
helicity. 3) it respects causality; 4) it is an irreducible representation of the Poincare group
(including parity) if and only if it is: a)real and b)massive with spin 1/2 or massless with
helicity 1/2. Finally, the energy positivity problem is discussed in a many-particles context.

**Category:** Mathematical Physics

[4] **viXra:1306.0231 [pdf]**
*submitted on 2013-06-28 19:36:33*

**Authors:** V. V.Dvoeglazov

**Comments:** 4 Pages. Presented in the DGFM-SMF School. December 2012. Puerto Vallarta, Mexico.

We construct self/anti-self charge conjugate (Majorana-like) states for the (1/2,0)+(0,1/2)$
representation of the Lorentz group, and their analogs for higher spins within the quantum field theory. The problem of the basis rotations and that of the selection of phases in the Dirac-like and Majorana-like field operators are considered. The discrete symmetries properties (P, C, T) are studied. Particular attention has been paid to the question of (anti)commutation of the Charge conjugation operator and the Parity in the helicity basis.
Dynamical equations have also been presented.
In the (1/2,0)+(0,1/2) representation
they obey the Dirac-like equation with eight components, which has been first introduced by Markov.
Thus, the Fock space for corresponding quantum fields is doubled (as shown by Ziino).
The chirality and the helicity
(two concepts which are frequently confused in the literature) for
Dirac and Majorana states have been discussed.

**Category:** Mathematical Physics

[3] **viXra:1306.0209 [pdf]**
*replaced on 2013-07-20 13:50:22*

**Authors:** Andrew Nassif

**Comments:** 15 Pages. Resubmitted, please see second PDF for better formatting

This is a collection of some of my notes in mathematical physics and Quantum Field Theory. This also includes the P vs. NP computational proof, the Zeta Function Data graphed, Notes on some common topics in Mathematics and Mathematical Physics, and Computational Mathematics as well as Three Dimensional Data Graphing.

**Category:** Mathematical Physics

[2] **viXra:1306.0050 [pdf]**
*submitted on 2013-06-07 17:37:51*

**Authors:** Dan Visser

**Comments:** 4 Pages.

I found a ‘quadruple image’ of ‘Hot and Cold Spots’ in the CMB-image, published by the gathered data of the Planck-satellite in 2013, and analyzed by me in the context of the (new) Double Torus cosmology. The ‘quadruple image’ proves the Universe rotates!! The ‘quadruple image’ follows the logic of a ‘dark flow’ in the Double Torus. This ‘dark flow’ is expressed in my (new) dark energy force-formula and astronomically determined. Hence, the Double Torus (until now a hypothesis), is changing into “hitting the right spot”, or in other words: “starts being a real model” !! The new cosmology is extensively described in a series of papers of mine, hosted in the vixra-archive in the category Mathematical Physics.

**Category:** Mathematical Physics

[1] **viXra:1306.0026 [pdf]**
*replaced on 2014-07-12 05:49:35*

**Authors:** Sergey A. Kamenshchikov

**Comments:** 8 Pages. Published unaltered at Chaos and Complexity Letters, Volume 8, Issue 1, 2014, pp. 63-71. Author: ru.linkedin.com/pub/sergey-kamenshchikov/60/8b1/21a/

Evolution of arbitrary stochastic system was considered in frame of phase transition description. Concept of Reynolds parameter of hydrodynamic motion was extended to arbitrary complex system. Basic phase parameter was expressed through power of energy, injected into system and power of energy, dissipated through internal nonlinear mechanisms. It was found out that basic phase parameter as control parameter must be delimited for two types of system - accelerator and decelerator. It was suggested to select zero state entropy on through condition of zero value for entropy production. Zero state introduces universal principle of disorder characterization. On basis of self organization S – theorem we have derived relations for entropy production behavior in the vicinity stationary state of system. Advantage of these relations in comparison to classical Prigogine theorem is versatility of their application to arbitrary nonlinear systems. It was found out that extended Prigogine theorem introduces two relations for accelerator and decelerator correspondingly, which remarks their quantitative difference. At the same time classic Prigogine theorem makes possible description of linear decelerator only. For unstable motion it corresponds to strange attractor.

**Category:** Mathematical Physics