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Register a new userThe Effective Dirac Algebra by Interaction Gauge Field
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B.T.T.Wong
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Conventional quantum field theory (QFT) is set on flat Minkowski spacetime, where all computable quantities are calculated from the flat metric $eta_{mu u}$. We can redefine the metric of spacetime from the Dirac algebra. In this paper, we study how an quantum electrodynamic interaction can alter the normal gamma matrix to an effective one and result in a shift in the metric perturbatively. We also study how the spin operator is changed under the interaction that contribute to an effective spin operator.
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In this paper we consider a model of Poincare gauge theory (PGT) in which a translational gauge field and a Lorentz gauge field are actually identified with the Einsteins gravitational field and a pair of ``Yang-Mills field and its partner, respectively.In this model we re-derive some special solutions and take up one of them. The solution represents a ``Yang-Mills field without its partner field and the Reissner-Nordstrom type spacetime, which are generated by a PGT-gauge charge and its mass.It is main purpose of this paper to investigate the interaction of massless Dirac fields with those fields. As a result, we find an interesting fact that the left-handed massless Dirac fields behave in the different manner from the right-handed ones. This can be explained as to be caused by the direct interaction of Dirac fields with the ``Yang-Mills field. Accordingly, the phenomenon can not happen in the behavior of the neutrino waves in ordinary Reissner-Nordstrom geometry. The difference between left- and right-handed effects is calculated quantitatively, considering the scattering problems of the massless Dirac fields by our Reissner-Nordstrom type black-hole.
The internal degrees of freedom of fermions are in the spin-charge-family theory described by the Clifford algebra objects, which are superposition of an odd number of $gamma^a$s. Arranged into irreducible representations of eigenvectors of the Cartan subalgebra of the Lorentz algebra $S^{ab}$ $(= frac{i}{2} gamma^a gamma^b|_{a e b})$ these objects form $2^{frac{d}{2}-1}$ families with $2^{frac{d}{2}-1}$ family members each. Family members of each family offer the description of all the observed quarks and leptons and antiquarks and antileptons, appearing in families. Families are reachable by $tilde{S}^{ab}$ $=frac{1}{2} tilde{gamma}^a tilde{gamma}^b|_{a e b}$. Creation operators, carrying the family member and family quantum numbers form the basic vectors. The action of the operators $gamma^a$s, $S^{ab}$, $tilde{gamma}^a$s and $tilde{S}^{ab}$, applying on the basic vectors, manifests as matrices. In this paper the basic vectors in $d=(3+1)$ Clifford space are discussed, chosen in a way that the matrix representations of $gamma^a$ and of $S^{ab}$ coincide for each family quantum number, determined by $tilde{S}^{ab} $, with the Dirac matrices. The appearance of charges in Clifford space is discussed by embedding $d=(3+1)$ space into $d=(5+1)$-dimensional space.
In this document, we briefly introduce the effective field theories. We propose some novel ideas in this manuscript. We introduce a novel formalism of the effective field theories and we apply it to the effective field theories of large scale structures. The new formalism is based on functionals of the actions composing those theories. We discuss our findings in a Cosmological Gravitology framework. We present with a cosmological inference approach these results and we give a guideline of how we can disentangle the best candidate between those models with some latest understanding of model selection.
In the Dirac theory of the quantum-mechanical interaction of a magnetic monopole and an electric charge, the vector potential is singular from the origin to infinity along certain direction - the so called Dirac string. Imposing the famous quantization condition, the singular string attached to the monopole can be rotated arbitrarily by a gauge transformation, and hence is not physically observable. By deriving its analytical expression and analyzing its properties, we show that the gauge function $chi({bf r})$ which rotates the string to another one has quite complicated behaviors depending on which side from which the position variable ${bf r}$ gets across the plane expanded by the two strings. Consequently, some misunderstandings in the literature are clarified.
If the Standard Model is understood as the first term of an effective field theory, the anomaly-cancellation conditions have to be worked out and fulfilled order by order in the effective field-theory expansion. We bring attention to this issue and study in detail a subset of the anomalies of the effective field theories at the electroweak scale. The end result is a set of sum rules for the operator coefficients. These conditions, which are necessary for the internal consistency of the theory, lead to a number of phenomenological consequences when implemented in analyses of experimental data. In particular, they not only decrease the number of free parameters in different physical processes but have the potential to relate processes with different flavor content. Conversely, a violation of these conditions would necessarily imply the existence of undetected non-decoupling new physics associated with the electroweak energy scale.
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