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Register a new userSpinors of Spin-one-half Fields
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Kevin Cahill
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This paper reviews how a two-state, spin-one-half system transforms under rotations. It then uses that knowledge to explain how momentum-zero, spin-one-half annihilation and creation operators transform under rotations. The paper then explains how a spin-one-half field transforms under rotations. The momentum-zero spinors are found from the way spin-one-half systems transform under rotations and from the Dirac equation. Once the momentum-zero spinors are known, the Dirac equation immediately yields the spinors at finite momentum. The paper then shows that with these spinors, a Dirac field transforms appropriately under charge conjugation, parity, and time reversal. The paper also describes how a Dirac field may be decomposed either into two 4-component Majorana fields or into a 2-component left-handed field and a 2-component right-handed field. Wigner rotations and Weinbergs derivation of the properties of spinors are also discussed.
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We present a simple and flexible method of keeping track of the complex phases and spin quantization axes for half-spin initial- and final-state Weyl spinors in scattering amplitudes of Standard Model high energy physics processes. Both cases of massless and massive spinors are discussed. The method is demonstrated and checked numerically for spin correlations in tau tau-bar production and decay. Its main application will be in the forthcoming work of combining effects due to multiple photon emission (exponentiation) and spin, embodied in the Monte Carlo event generators for production and decay of unstable fermions such as the tau lepton, t-quark and hypothetical new heavy particles.
In this work we analyze the zero mode localization and resonances of $1/2-$spin fermions in co-dimension one Randall-Sundrum braneworld scenarios. We consider delta-like, domain walls and deformed domain walls membranes. Beyond the influence of the spacetime dimension $D$ we also consider three types of couplings: (i) the standard Yukawa coupling with the scalar field and parameter $eta_1$, (ii) a Yukawa-dilaton coupling with two parameters $eta_2$ and $lambda$ and (iii) a dilaton derivative coupling with parameter $h$. Together with the deformation parameter $s$, we end up with five free parameter to be considered. For the zero mode we find that the localization is dependent of $D$, because the spinorial representation changes when the bulk dimensionality is odd or even and must be treated separately. For case (i) we find that in odd dimensions only one chirality can be localized and for even dimension a massless Dirac spinor is trapped over the brane. In the cases (ii) and (iii) we find that for some values of the parameters, both chiralities can be localized in odd dimensions and for even dimensions we obtain that the massless Dirac spinor is trapped over the brane. We also calculated numerically resonances for cases (ii) and (iii) by using the transfer matrix method. We find that, for deformed defects, the increasing of $D$ induces a shift in the peaks of resonances. For a given $lambda$ with domain walls, we find that the resonances can show up by changing the spacetime dimensionality. For example, the same case in $D=5$ do not induces resonances but when we consider $D=10$ one peak of resonance is found. Therefore the introduction of more dimensions, diversely from the bosonic case, can change drastically the zero mode and resonances in fermion fields.
Spinor fields are considered in a generally covariant environment where they can be written in the polar form. The polar form is the one in which spinorial fields are expressed as a module times the exponential of a complex pseudo-phase, and in this form the full spinorial field theory can in turn be expressed by employing only real tensorial quantities. Such a reformulation makes it possible to emphasize properties of the spinorial field theory, and this would enrich our understanding in ways that have never been followed up until this moment.
In this paper we proceed into the next step of formalization of a consistent dual theory for mass dimension one spinors. This task is developed approaching the two different and complementary aspects of such duals, clarifying its algebraic structure and the so called $tau-$deformation. The former regards the mathematical equivalence of the recent proposed Lorentz preserving dual with the duals of algebraic spinors, from Clifford algebras, showing the consistency and generality of the new dual. Moreover, by revealing its automorphism structure, the hole of the $tau-$deformation and contrasting the action group orbits with other Lorentz breaking scenarios, we argue that the new mass dimension one dual theory is placed over solid and consistent basis.
A new localization scheme for Klein-Gordon particle states is introduced in the form of general space and time operators. The definition of these operators is achieved by establishing a second quantum field in the momentum space of the standard field we want to localize (here Klein-Gordon field). The motivation for defining a new field in momentum space is as follows. In standard field theories one can define a momentum (and energy) operator for a field excitation but not a general position (and time) operator because the field satisfies a differential equation in position space and, through its Fourier transform, an algebraic equation in momentum space. Thus, in a field theory which does the opposite, namely it satisfies a differential equation in momentum space and an algebraic equation in position space, we will be able to define a position and time operator. Since the new field lives in the momentum space of the Klein-Gordon field, the creation/annihilation operators of the former, which build the new space and time operators, reduce to the field operators of the latter. As a result, particle states of Klein-Gordon field are eigenstates of the new space and time operators and therefore localized on a space-time described by their spectrum. Finally, we show that this space-time is flat because it accommodates the two postulates of special relativity. Interpretation of special relativistic notions as inertial observers and proper acceleration in terms of the new field is also provided.
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