We study the properties of the mass gap for monopole solutions in SU(2) Yang-Mills theory with a source of the non-Abelian gauge field in the form of a spinor field described by the nonlinear Dirac equation. Different types of nonlinearities parameterized by the parameter $λ$ are under consideration. It is shown that for the range of values of this parameter studied in the present paper the value of the mass gap depends monotonically on this parameter, and the position of the mass gap does not practically depend on $λ$.
Monopole solutions in SU(2) Yang-Mills theory which includes spinor fields described by the nonlinear Dirac equation are obtained. It is demonstrated that the energy spectrum of such a system possesses a global minimum whose appearance is brought about solely by the nonlinear spinor fields. It is shown that the monopole solution obtained differs in principle from the 't~Hooft-Polyakov monopole in that it is topologically trivial.
Within SU(2) Yang-Mills theory with a source of the non-Abelian gauge field in the form of a classical spinor field, we study the dependence of the mass gap on the coupling constant between the gauge and nonlinear spinor fields. It is shown that the total dimensionless energy of the monopole interacting with the nonlinear spinor fields depends only on the dimensionless coupling constant.
Four-dimensional N=1 supersymmetric Spin(N) gauge theories with matter in the vector and spinor representations are considered. Dual descriptions are known for some of these theories. It is noted that when masses are given to all fields in the spinor representation, the dual gauge group G breaks to a group H such that π_2(G/H)=Z_2. The quantum numbers of the associated Z_2 monopole and those of the massive spinors are shown to agree, suggesting that the monopole is the image of the massive spinors under duality. It follows that electric sources in the spinor representation, needed as test char…
An "expanded" description is introduced to examine the spinor-monopole identification proposed by Strassler for four-dimensional $\cal N$ = 1 supersymmetric Spin(10) gauge theories with matter in F vector and N spinor representations. It is shown that a Z_2 monopole in the "expanded" theory is associated with massive spinors of the Spin(10) theory. For N=2, two spinor case, we confirm this identification by matching the transformation properties of the two theories under SU(2) flavor symmetry. However, for N $\ge$ 3, the transformation properties are not matched between the spinors and the mon…
We show how the length scale hierarchy, resulting from different interaction strengths in an optically-trapped spin-1 sodium-23 Bose-Einstein condensate, can lead to intriguing core deformations in singular topological defects. In particular, a point defect can be unstable with respect to the formation of a stable half-quantum vortex ring (an Alice ring), providing a realistic scheme to use dissipation as a sophisticated state engineering tool. We compute the threshold for stability of the point monopole, which is beyond the current experimental regime.
I use Unified Spinor Fields (USF), to discuss the creation of magnetic monopoles during preinflation, as excitations of the quantum vacuum coming from a condensate of massive charged vector bosons. For a primordial universe with total energy $M_p$, and for magnetic monopoles created with a total Planck magnetic charge $q_M=q_P=\pm e/\sqrtα$ and a total mass $m_M$, it is obtained after quantisation of the action that the fine-structure constant is given by: $α= \frac{5}{6} \left(1- \frac{16 \,m_M}{5 \,M_p}\right) \,\left(\frac{e}{q_M}\right)^2$. If these magnetic monopoles were with total magne…
We investigate the vacuum expectation values of the energy-momentum tensor and the fermionic condensate associated with a massive spinor field obeying the MIT bag boundary condition on a spherical shell in the global monopole spacetime. In order to do that it was used the generalized Abel-Plana summation formula. As we shall see, this procedure allows to extract from the vacuum expectation values the contribution coming from to the unbounded spacetime and explicitly to present the boundary induced parts. As to the boundary induced contribution, two distinct situations are examined: the vacuum …
We formulate an interacting theory of a vector-spinor field that gauges anticommuting spinor charges \{Q_α^I, Q_β^J \} = 0 in arbitrary space-time dimensions. The field content of the system is (ψ_μ^{αI}, χ^{αI J}, A_μ^I), where ψ_μ^{αI} is a vector-spinor in the adjoint representation of an arbitrary gauge group, and A_μ^I is its gauge field, while χ^{αI J} is an extra spinor with antisymmetric adjoint indices I J. Amazingly, the consistency of the vector-spinor field equation is maintained, despite its non-trivial interactions.
By taking the interacting spinor-scalar theory on the $AdS_{d+1}$ space we calculate the boundary CFT correlation functions using AdS/CFT correspondence.
Consistent interactions of spin 3/2 field that realize a nilpotent spinorial symmetry are presented. Based on our previous results on purely bosonic non-Abelian tensor with consistent interactions, we present a new system for interacting spin 3/2 field that realizes the nilpotent fermionic symmetry.
We discuss the possible relevance of some recent mathematical results and techniques on four-manifolds to physics. We first suggest that the existence of uncountably many R^4's with non-equivalent smooth structures, a mathematical phenomenon unique to four dimensions, may be responsible for the observed four-dimensionality of spacetime. We then point out the remarkable fact that self-dual gauge fields and Weyl spinors can live on a manifold of Euclidean signature without affecting the metric. As a specific example, we consider solutions of the Seiberg-Witten Monopole Equations in which the U(1…
In this paper we recall that by construction Elko spinor fields of λ and ρ types satisfy a coupled system of first order partial differential equations (csfopde) that once interacted leads to Klein-Gordon equations for the λ and ρ type fields. Since the csfopde is the basic one and since the Klein-Gordon equations for λ and ρ possess solutions that are not solutions of the csfopde for λ and ρ we infer that it is legitimate to attribute to those fields mass dimension 3/2 (as is the case of Dirac spinor fields) and not mass dimension 1 as previously suggested in recent literature (see list of re…
In this paper we investigate the vacuum polarization effects associated with a massive fermionic field due to the non-trivial topology of the global monopole spacetime and boundary conditions imposed on this field. Specifically we investigate the vacuum expectation values of the energy-momentum tensor and fermionic condensate admitting that the field obeys the MIT bag boundary condition on two concentric spherical shells. In order to develop this analysis, we use the generalized Abel-Plana summation, which allows to extract from the vacuum expectation values the contribution coming from a sing…
We provide a theory with a monopole of a strongly-interacting hidden U(1) gauge symmetry that can explain the 750-GeV diphoton excess reported by ATLAS and CMS. The excess results from the resonance of monopole, which is produced via gluon fusion and decays into two photons. In the low energy, there are only mesons and a monopole in our model because any baryons cannot be gauge invariant in terms of strongly interacting Abelian symmetry. This is advantageous of our model because there is no unwanted relics around the BBN epoch.
We show that we can construct a model in 3+1 dimensions where only composite scalars take place in physical processes as incoming and outgoing particles, whereas constituent spinors only act as intermediary particles. Hence while the spinor-spinor scattering goes to zero, the scattering of composites gives nontrivial results.
We study quantum systems of interacting electrons, magnetic monopoles, and electromagnetic field. We formulate a convenient field theory, in which the electron-photon, monopole-photon, and electron-monopole interactions take simple forms.
A gauge transformation provided by the three eigenfunctions of $\B^a(x) \cdot \B^b(x)$ (where $\B^a(x)$, with a=1,2,3, are the non-Abelian magnetic fields) exposes the topological configurations of the Yang-Mills fields. In particular, it gives Dirac monopoles interacting with `photons' and massless charged vector bosons. A magnetic dipole field at each monopole corresponds to infinitesimal translation of the monopole, and provides the functional measure a la collective coordinates. The grand canonical partition function of the monopole plasma is exactly equivalent to a local field theory with…
We show that we can construct a model in 3+1 dimensions where it is necessary that composite vector particles take place in physical processes as incoming and outgoing particles . Cross-section of the processes in which only the constituent spinors take place goes to zero. While the spinor-spinor scattering goes to zero, the scattering of composites gives nontrivial results.
A new classical 2-spinor approach to $U(1)$ gauge theory is presented in which the usual four-potential vector field is replaced by a symmetric second rank spinor. Following a lagrangian formulation, it is shown that the four-rank spinor representing the Maxwell field tensor has a $U(1)$ local gauge invariance in terms of the electric and magnetic field strengths. When applied to the magnetic field of a monopole, this formulation, via the irreducible representations condition for the gauge group, leads to a quantization condition differing by a factor 2 of the one predicted by Dirac without re…
Monopole field configurations have been extensively studied in both Abelian and non-Abelian gauge theories. The question of the quantum corrections to these systems is a difficult one, since the classical monopoles have non-perturbatively large couplings, which makes the standard, perturbative methods for calculating quantum corrections suspect. Here we apply a modified version of Heisenberg's quantization technique for strongly interacting, nonlinear fields to a classical solution of the SU(3) Yang-Mills field equations. This classical solution is not monopole-like and has an energy density w…
In 1994, Witten has defined a monopole invariant and he has shown the equivalence of this invariant with Donaldson's polynomial using his result in \( \SS \)-duality. This new invariant is very powerful because the gauge group is abelian. By using such an invariant, many new results are found in the smooth, Kähler and even the symplectic categories. However, almost every paper in this topic write the monopole equations in a different way. Therefore is it necessary to clarify the basic idea behind the definition of such an invariant. In this paper we investigate the algebraic structure (Cliffor…
Metric spinor phase of the Infeld-van der Waerden γ-formalism and axion field were identified in Ref. [1], by using Maxwell theory. Since axion couples with fermions, we will investigate Dirac theory to extend the work given in [1], showing that is possible again to identify this phase with the axion. By searching an exact identification, we will work yet the spin transformations to adapt chiral rotations and so to show that the metric spinor phase behaves exactly as required for the axion field. We will study also the Dirac-Maxwell system which provides a minimal Lagrangian approach for the a…
In this paper we present the effects produced by the temperature in the renormalized vacuum expectation value of the zero-zero component of the energy-momentum tensor associated with massless left-handed spinor field in the pointlike global monopole spacetime. In order to develop this calculation we had to obtain the Euclidean thermal Green function in this background. Because the expression obtained for the thermal energy density cannot be expressed in a closed form, its explicit dependence on the temperature is not completely evident. So, in order to obtain concrete information about its the…
We present unique solutions of the Seiberg-Witten Monopole Equations in which the U(1) curvature is covariantly constant, the monopole Weyl spinor consists of a single constant component, and the 4-manifold is a product of two Riemann surfaces of genuses p_1 and p_2. There are p_1 -1 magnetic vortices on one surface and p_2 - 1 electric ones on the other, with p_1 + p_2 \geq 2 p_1 = p_2= 1 being excluded). When p_1 = p_2, the electromagnetic fields are self-dual and one also has a solution of the coupled euclidean Einstein-Maxwell-Dirac equations, with the monopole condensate serving as cosmol…
We study the systems of scalar and spinor particles with mixing emitted by external classical sources. The particles wave functions exactly accounting for external sources are obtained directly from the Lorentz invariant wave equations in (3+1)-dimensional space-time. Then we discuss sources which are localized in space and emit harmonic radiation. We obtain that the considered scalar and spinor fields can be converted from one type to another due to the presence of the vacuum mixing. This phenomenon is shown to be analogous to neutrino flavor oscillations in vacuum since the calculated transi…
Within the context of the extended bi-spinor gauge theory we describe a new off-shell realization of scalar supersymmetry (s-susy) of massless interacting fields with U(1), U(1) x SU(N) and U(1) x SU(N_1) x SU(N_2) gauge groups. S-susy acts in the space of graded differential forms. The realization is non-linear in the non-abelian case. S-susy would not require the doubling of the SM particle spectrum. Instead, essentially only the forth generation of quarks and leptons would be needed as extra field content. The theory is by construction globally U(2,2) invariant and is an example of a supers…
In this paper, we study the Seiberg-Witten equations on a compact 3-manifold with boundary. Solutions to these equations are called monopoles. Under some simple topological assumptions, we show that the solution space of all monopoles is a Banach manifold in suitable function space topologies. We then prove that the restriction of the space of monopoles to the boundary is a submersion onto a Lagrangian submanifold of the space of connections and spinors on the boundary. Both these spaces are infinite dimensional, even modulo gauge, since no boundary conditions are specified for the Seiberg-Wit…
We study the classical and quantum cosmology of a universe in which the matter source is a massive Dirac spinor field and consider cases where such fields are either free or self-interacting. We focus attention on the spatially flat Robertson-Walker cosmology and classify the solutions of the Einstein-Dirac system in the case of zero, negative and positive cosmological constant $Λ$. For $Λ<0$, these solutions exhibit signature transitions from a Euclidean to a Lorentzian domain. In the case of massless spinor fields it is found that signature changing solutions do not exist when the field is f…
Within the context of the Abelian Projection of QCD monopole-like quantum excitations of gauge fields are studied. We start with certain classical solutions, of the SU(2) Yang-Mills field equations, which are not monopole-like and whose energy density diverges as $r \to \infty$. These divergent classical solutions are then quantized using a modified version of Heisenberg's quantization technique for strongly interacting, nonlinear fields. The modified Heisenberg quantization technique leads to a system of equations with mixed quantum and classical degrees of freedom. By applying a Feynman path…
We describe a new realization of both global and local supersymmetry acting in spaces of commuting and anticommuting differential forms. Unlike the standard supersymmetry, it has Lorentz scalar transformation parameters. It is related but is not reducible to standard supersymmetry. Reformulation of the Standard Model with the new supersymmetry, called scalar supersymmetry, can be achieved with the particle content of the SM. BRST symmetry is extended to include scalar supersymmetry multiplets. Linear realization of scalar supersymmetry with free fields or with fields interacting with backgroun…
The non-relativistic `Dirac' equation of Lévy-Leblond is used to describe a spin {\small 1/2} particle interacting with a Chern-Simons gauge field. Static, purely magnetic, self-dual spinor vortices are constructed. The solution can be `exported' to a uniform magnetic background field.
We quantize the interaction of gravity with Yang-Mills and spinor fields, hence offering a quantum theory incorporating all four fundamental forces of nature. Using canonical quantization we obtain solutions of the Wheeler-DeWitt equation in a vector bundle and the method of second quantization leads to a symplectic vector space $(V,\om)$ and a corresponding CCR representation for the bosonic components and a CAR representation for the fermionic part. The solution space of the Wheeler-DeWitt equation is invariant under gauge transformations and under isometries in the spacelike base space $\so…
The Maxwell-covariant particle model is formulated in tensorial extended D=4 space-time (x_mu, z_{mu nu}) parametrized by ten-dimensional coset of D=4 Maxwell group, with added auxiliary Weyl spinors lambda_alpha, y^alpha. We provide the Hamiltonian quantization of the model and demonstrate that first class constraints modify the known equations obtained for massless higher spin fields in flat tensorial space-time. We obtain the Maxwell-covariant field equations for new infinite dimensional spin multiplets. The component fields assigned to different spin values are linked by couplings proporti…
We compute gauge theories of the Lorentz group. We discuss non-interacting, and interacting fermionic systems. The interacting system combines a local with a global Lorentz group, i.e, discusses a $SO(3,1)_{l}\times SO(3,1)_{g}$-theory. We compute the equations of motion and conservation laws for the fermionic matter current. The core of our work is the prediction of some new form of monopoles we call 'Dirac-Clifford-'t Hooft-Polyakov'-monopole. It resides in a state similar to color-flavor locking. Dirac-Clifford-'t Hooft-Polyakov-monopoles are invariant under global Lorentz transformations a…
We extend our program, of coupling theories to scale in order to make their Weyl invariance manifest, to include interacting theories, fermions and supersymmetric theories. The results produce mass terms coinciding with the standard ones for universes that are Einstein, but are novel in general backgrounds. They are generalizations of the gravitational couplings of a conformally improved scalar to fields with general scaling and tensor properties. The couplings we find are more general than just trivial ones following from the conformal compensating mechanisms. In particular, in the setting wh…
Eigenfunctions of total angular momentum for a charged vector field interacting with a magnetic monopole are constructed and their properties studied. In general, these eigenfunctions can be obtained by applying vector operators to the monopole spherical harmonics in a manner similar to that often used for the construction of the ordinary vector spherical harmonics. This construction fails for the harmonics with the minimum allowed angular momentum. These latter form a set of vector fields with vanishing covariant curl and covariant divergence, whose number can be determined by an index theore…
We study the classical and quantum cosmology of a 4+1-dimensional space-time with a non-zero cosmological constant coupled to a self interacting massive spinor field. We consider a spatially flat Robertson-Walker universe with the usual scale factor $R(t)$ and an internal scale factor $a(t)$ associated with the extra dimension. For a free spinor field the resulting equations admit exact solutions, whereas for a self interacting spinor field one should resort to a numerical method for exhibiting their behavior. These solutions give rise to a degenerate metric and exhibit signature transition fr…
It is shown that the non-relativistic `Dirac' equation of Lévy-Leblond, we used recently to describe a spin $1/2$ field interacting non-relativistically with a Chern-Simons gauge field, can be obtained by lightlike reduction from $3+1$ dimensions. This allows us to prove that the system is Schrödinger symmetric. A spinor representation of the Schrödinger group is presented. Static, self-dual solutions, describing spinor vortices are given and shown to be the non-relativistic limits of the fermionic vortices found by Cho et al. The construction is extended to external harmonic and uniform magne…
We present simulations of one magnetic monopole interacting with multiple magnetic singularities. Three-dimensional plots of the energy density are constructed from explicit solutions to the Bogomolny equation obtained by Blair, Cherkis, and Durcan. Animations follow trajectories derived from collective coordinate mechanics on the multi-centered Taub--NUT monopole moduli space. We supplement our numerical results with a complete analytic treatment of the single-defect case.
A new model for monopole catalysis of nucleon decay is proposed. Unlike in the earlier one, the only light fields in this model are the photon and Skyrme (pion) field. The model admits the 't Hooft- Polyakov monopole and Skyrmion as classical solutions, while baryon number non-conservation occurs through an anomaly involving an intermediate mass axial vector field resembling W- and Z-bosons. By considering spherically symmetric monopole-Skyrmion configurations, we find that the Skyrmion looses essentially all its mass when interacting with the monopole, which is phenomenologically identical to…
We present a "primitive" way of realizing finite-mass Dirac monopoles in $U(1)$ gauge theories involving a single non-minimally interacting scalar field. Typically, the energy density of this type of monopole is not concentrated at its core, but it is distributed in a spherical shell, as we illustrate on several exact solutions in the Bogomol'nyi-Prasad-Sommerfield (BPS) limit. We show that our construction can be interpreted as a limit of infinitely massive $W$ bosons coupled to electromagnetic field-strength via a dipole moment. Combining our approach with ideas of Weinberg and Lee, we prese…
In a new Weyl 2-spinor approach to Non abelian Gauge Theories, starting with the local U(1) Gauge group of a previous work, we study now the SU(3) case corresponding to quarks (antiquarks) interacting with color fields. The principal difference with the conventional approach is that particle-field interactions are not described by means of potentials but by the field strength magnitudes. Some analytical expressions showing similarities with electrodynamics are obtained. Classical equations that describe the behavior of quarks under gluon fields might be in principle applied to the quark-gluon …
We formulate a Euclidean lattice theory of interacting elementary spin-half electric and magnetic charges, which we refer to as electrons and magnetic monopoles respectively. The model uses the polymer representation of the fermion determinant, and exhibits a self-dual symmetry provided electric charge $e$ and magnetic charge $g$ obey the minimal Dirac quantisation condition $eg=2π$. In a hopping parameter expansion at lowest order, we show that virtual electron and monopole loops contribute radiative corrections of opposite sign to the photon propagator. We argue that in the limit $e\to0$, fe…
It is shown that, in the theory of interacting Yang -Mills fields and a Higgs field, there is a topological degeneracy of Bogomol'nyi-Prasad-Sommerfield (BPS) monopoles and that there arises, in this case, a chromoelectric monopole characterized by a new topological variable that describes transitions between topological states of the monopole in the Minkowski space (in just the same way as an instanton describes such transitions in the Euclidean space). The limit of an infinitely large mass of the Higgs field at a finite density of the BPS monopole is considered as a model of the stable vacuu…
In the framework of the Einstein-Dirac-axion-aether theory we consider the quartet of self-interacting cosmic fields, which includes the dynamic aether, presented by the unit timelike vector field, the axionic dark mater, described by the pseudoscalar field, the spinor field associated with fermion particles, and the gravity field. The key, associated with the mechanism of self-interaction, is installed into the modified periodic potential of the pseudoscalar (axion) field constructed on the base of a guiding function, which depends on one invariant, one pseudo-invariant and two cross-invarian…
We studied (arxiv: 1001.4679, 1205.1714) properties of spinors in a toy model in $d=(1+5)$ as a step towards realistic Kaluza-Klein (like) theories in non compact spaces. ${\cal M}^{(5+1)}$ was assumed to break to an infinite disc with a zweibein which makes a disc curved on $S^2$ and with a spin connection field which allows on such a sphere only one massless spinor state. This time we are taking into account families of spinors interacting with several spin connection fields, as required for this toy model by the spin-charge-family theory We are studying possible masslesness of families of s…
