arXiv subjects

Matej Pavšič

Publications and source records attributed to Matej Pavšič.

At least 19 recordsLinked to original sources

arXiv2022

A New Perspective on Quantum Field Theory Revealing Possible Existence of Another Kind of Fermions Forming Dark Matter

Quantum fields are considered as generators of infinite-dimensional Clifford algebra $Cl(\infty)$, which can be either orthogonal (in case of fermions) or symplectic (in case of bosons). A generic quantum state can be expressed as a superposition of the basis elements of $Cl(\infty)$, the superposition coefficients being multiparticle complex-valued wave functions. The basis elements, that are products of the generators of $Cl(\infty)$ in the Witt basis, act as creation and annihilation operators. They create positive and negative energy states that include the bare and the Dirac vacuum as special cases. It is shown that the nonvanishing electric charge arises from an extra dimension or from doubling the number of creation and annihilation operators, which brings an extra imaginary unit ${\bar i}$ into the description. A further extension is to consider the ${\bar i}$ as one of the quaternionic imaginary units and consider a generic state as having values in the quaternionic algebra or, equivalently, in the complexified 2-dimensional Clifford algebra, $Cl(2)\otimes C$.contains two distinct fundamental representations of $SU(2)$, one associated with the weak isospin oublet $(ν_e,e^-)$, and the other one with the doublet of new leptons, denoted $(ε^+,ν_ε)$, that together with the new quarks $(u',d')$ can be identified with dark matter.

physics.gen-ph↗

arXiv2022

A Novel Approach to Quantum Gravity in the Presence of Matter without the Problem of Time

An approach to the quantization of gravity in the presence matter is examined which starts from the classical Einstein-Hilbert action and matter approximated by "point" particles minimally coupled to the metric. Upon quantization, the Hamilton constraint assumes the form of the Schrödinger equation: it contains the usual Wheeler-DeWitt term and the term with the time derivative of the wave function. In addition, the wave function also satisfies the Klein-Gordon equation, which arises as the quantum counterpart of the constraint among particles' momenta. Comparison of the novel approach with the usual one in which matter is represented by scalar fields is performed, and shown that those approaches do not exclude, but complement each other. In final discussion it is pointed out that the classical matter could consist of superparticles or spinning particles, described by the commuting and anticommuting Grassmann coordinates, in which case spinor fields would occur after quantization.

physics.gen-ph↗

arXiv2021

Clifford Algebras, Spinors and $Cl(8,8)$ Unification

It is shown how the vector space $V_{8,8}$ arises from the Clifford algebra $Cl(1,3)$ of spacetime. The latter algebra describes fundamental objects such as strings and branes in terms of their $r$-volume degrees of freedom, $x^{μ_1 μ_2 ...μ_r}$ $\equiv x^M$, $r=0,1,2,3$, that generalizethe concept of center of mass. Taking into account that there are sixteen $x^M$, $M=1,2,3,...,16$, and in general $16 \times 15/2 = 120$ rotations of the form $x'^M = {R^M}_N x^N$, we can consider $x^M$ as components of a vector $X=x^M q_M$, where $q_M$ are generators of the Clifford algebra $Cl(8,8)$. The vector space $V_{8,8}$ has enough room for the unification of the fundamental particles and forces of the standard model. The rotations in $V_{8,8}\otimes \mathbb{C}$ contain the grand unification group $SO(10)$ as a subgroup, and also the Lorentz group $SO(1,3)$. It is shown how the Coleman-Mandula no go theorem can be avoided. Spinors in $V_{8,8}\otimes \mathbb{C}$ are constructed in terms of the wedge products of the basis vectors rewritten in the Witt basis. They satisfy the massless Dirac equation in $M_{8,8}$ with the internal part of the Dirac operator giving the non vanishing masses in four dimensions.

hep-th↗

arXiv2021

On the Coupling of Relativistic Particle to Gravity and Wheeler-DeWitt Quantization

A system consisting of a point particle coupled to gravity is investigated. The set of constraints is derived. It was found that a suitable superposition of those constraints is the generator of the infinitesimal transformations of the time coordinate $t\equiv x^0$ and serves as the Hamiltonian which gives the correct equations of motion. Besides that, the system satisfies the mass shell constraint, $p^μp_μ- m^2 = 0$, which is the generator of the worldsheet reparametrizations, where the momenta $p_μ$, $μ=0,1,2,3$, generate infinitesimal changes of the particle's position $X^μ$ in spacetime. Consequently, the Hamiltonian contains $p_0$, which upon quantization becomes the operator $- i \partial/\partial T$, occurring on the r.h.s. of the Wheeler-DeWitt euqtion. Here the role of time has the particle coordinate $X^0 \equiv T$, which is a distinct concept than the spacetime coordinate $x^0 \equiv t$. It is also shown how the ordering ambiguities can be avoided if a quadratic form of the momenta is cast into the form that instead of the metric contains the basis vectors.

gr-qc↗

arXiv2020

On Negative Energies, Strings, Branes, and Braneworlds: A Review of Novel Approaches

On the way towards quantum gravity and the unification of interaction, several ideas have been rejected and avenues avoided because they were perceived as physically unviable. But in the literature there are works in which it was found the contrary, namely that those rejected topics make sense after all. Such topics, reviewed in this article, are negative energies occurring in higher derivative theories and ultrahyperbolic spaces, ordering ambiguity of operators in curved spaces, the vast landscape of possible compactifications of extra dimensions in string theory, and quantization of a 3-brane in braneworld scenarios.

hep-th↗

arXiv2019

A Novel View on Successive Quantizations, Leading to Increasingly More "Miraculous" States

A series of successive quantizations is considered, starting with the quantization of a non relativistic or relativistic point particle: 1) quantization of a particle's position, 2) quantization of wave function, 3) quantization of wave functional. The latter step implies that the wave packet profiles forming the states of quantum field theory are themselves quantized, which gives new physical states that are configurations of configurations. In the procedure of quantization, instead of the Schrödinger first order equation in time derivative for complex wave function (or functional), the equivalent second order equation for its real part was used. In such a way, at each level of quantization, the equation a quantum state satisfies is just like that of a harmonic oscillator, and wave function(al) is composed in terms of the pair of its canonically conjugated variables.

hep-th↗

arXiv2018

Manifestly Covariant Canonical Quantization of the Scalar Field and Particle Localization

Particle localization within quantum field theory is revisited. Canonical quantization of a free scalar field theory is performed in a manifestly Lorentz covariant way with respect to an arbitrary 3-surface $Σ$, which is the simultaneity surface associated with the observer, whose proper time direction is orthogonal to $Σ$. Position on $Σ$ is determined by a 4-vector ${\bar x}^μ$. The corresponding quantum position operator, formed in terms of the operators $a^\dagger ({\bar x})$, $a({\bar x})$, that create/annihilate particles on $Σ$, has thus well behaved properties under Lorentz transformations. A generic state is a superposition of the states, created with $a^\dagger ({\bar x})$, the superposition coefficients forming multiparticle wave packet profiles---wave functions, including a single particle wave function that satisfies the covariant generalization of the Foldy equation. The covariant center of mass operator is introduced and its expectation values in a generic multiparticle state calculated.

hep-th↗

arXiv2018

Localized States in Quantum Field Theory

Localized states in relativistic quantum field theories are usually considered as problematic, because of their seemingly strange (non covariant) behavior under Lorentz transformations, and because they can spread faster than light. We point out that a careful quantum field theoretic analysis in which we distinguish between basis position states and wave packet states clarifies the issue of Lorentz covariance. The issue of causality is resolved by observing that superluminal transmission of information cannot be achieved by such wave packets. Within this context it follows that the Reef-Schlieder theorem, which proves that localized states can exhibit influence on each other over space like distances, does not imply that such states cannot exist in quantum field theory.

hep-th↗

arXiv2017

Quantized Fields à la Clifford and Unification

It is shown that the generators of Clifford algebras behave as creation and annihilation operators for fermions and bosons. They can create extended objects, such as strings and branes, and can induce curved metric of our spacetime. At a fixed point, we consider the Clifford algebra $Cl(8)$ of the 8-dimensional phase space, and show that one quarter of the basis elements of $Cl(8)$ can represent all known particles of the first generation of the Standard model, whereas the other three quarters are invisible to us and can thus correspond to dark matter.

physics.gen-ph↗

arXiv2017

Branes and Quantized Fields

It is shown that the Dirac-Nambu-Goto brane can be described as a point particle in an infinite dimensional space with a particular metric. This can be considered as a special case of a general theory in which branes are points in the brane space ${\cal M}$, whose metric is dynamical, just like in general relativity. Such a brane theory, amongst others, includes the flat brane space, whose metric is the infinite dimensional analog of the Minkowski space metric $η_{μν}$. A brane living in the latter space will be called "flat brane"; it is like a bunch of non-interacting point particles. Quantization of the latter system leads to a system of non-interacting quantum fields. Interactions can be included if we consider a non trivial metric in the space of fields. Then the effective classical brane is no longer a flat brane. For a particular choice of the metric in the field space we obtain the Dirac-Nambu-Goto brane. We also show how a Stueckelberg-like quantum field arises within the brane space formalism. With the Stueckelberg fields, we avoid certain well-known intricacies, especially those related to the position operator that is needed in our construction of effective classical branes from the systems of quantum fields.

hep-th↗

arXiv2016

A New Approach to the Classical and Quantum Dynamics of Branes

It is shown that the Dirac-nambu-Goto brane can be described as a point particle in an infinite dimensional brane space with a particular metric. This suggests a generalization to brane spaces with arbitrary metric, including the "flat" metric. Then quantization of such a system is straightforward: it is just like quantization of a bunch of non interacting particles. This leads us to a system of a continuous set of scalar fields. For a particular choice of the metric in the space of fields we find that the classical Dirac-Nambu-Goto brane theory arises as an effective theory of such an underlying quantum field theory. Quantization of branes is important for the brane world scenarios, and thus for "quantum gravity".

hep-th↗

arXiv2016

Pais-Uhlenbeck Oscillator and Negative Energies

We review the occurrence of negative energies in Pais-Uhlenbeck oscillator. We point out that in the absence of interactions negative energies are not problematic, neither in the classical nor in the quantized theory. However, in the presence of interactions that couple positive and negative energy degrees of freedom the system is unstable, unless the potential is bounded from bellow and above. We review some approaches in the literature that attempt to avoid the problem of negative energies in the Pais-Uhlenbeck oscillator.

gr-qc↗

arXiv2015

Point Particle with Extrinsic Curvature as a Boundary of a Nambu-Goto String: Classical and Quantum Model

It is shown how a string living in a higher dimensional space can be approximated as a point particle with squared extrinsic curvature. We consider a generalized Howe-Tucker action for such a "rigid particle" and consider its classical equations of motion and constraints. We find that the algebra of the Dirac brackets between the dynamical variables associated with velocity and acceleration contains the spin tensor. After quantization, the corresponding operators can be represented by the Dirac matrices, projected onto the hypersurface that is orthogonal to the direction of momentum. A condition for the consistency of such a representation is that the states must satisfy the Dirac equation with a suitable effective mass. The Pauli-Lubanski vector composed with such projected Dirac matrices is equal to the Pauli-Lubanski vector composed with the usual, non projected, Dirac matrices, and its eigenvalues thus correspond to spin one half states.

hep-th↗

arXiv2015

A Non-Trivial Zero Length Limit of the Nambu-Goto String

We show that a Nambu-Goto string has a nontrivial zero length limit which corresponds to a massless particle with extrinsic curvature. The system has the set of six first class constraints, which restrict the phase space variables so that the spin vanishes. Upon quantization, we obtain six conditions on the state, which can be represented as a wave function of position coordinates, $x^μ$, and velocities, $q^μ$. We have found a wave function $ψ(x,q)$ that turns out to be a general solution of the corresponding system of six differential equations, if the dimensionality of spacetime is eight. Though classically the system is just a point particle with vanishing extrinsic curvature and spin, the quantized system is not trivial, because it is consistent in eight, but not in arbitrary, dimensions.

hep-th↗

arXiv2014

On the Stueckelberg Like Generalization of General Relativity

We first consider the Klein-Gordon equation in the 6-dimensional space $M_{2,4}$ with signature $+ - - - - +$ and show how it reduces to the Stueckelberg equation in the 4-dimensional spacetime $M_{1,3}$. A field that satisfies the Stueckelberg equation depends not only on the four spacetime coordinates $x^μ$, but also on an extra parameter $τ$, the so called evolution time. In our setup, $τ$ comes from the extra two dimensions. We point out that the space $M_{2,4}$ can be identified with a subspace of the 16-dimensional Clifford space, a manifold whose tangent space at any point is the Clifford algebra Cl(1,3). Clifford space is the space of oriented $r$-volumes, $r=0,1,2,3$, associated with the extended objects living in $M_{1,3}$. We consider the Einstein equations that describe a generic curved space $M_{2,4}$. The metric tensor depends on six coordinates. In the presence of an isometry given by a suitable Killing vector field, the metric tensor depends on five coordinates only, which include $τ$. Following the formalism of the canonical classical and quantum gravity, we perform the 4 + 1 decomposition of the 5-dimensional general relativity and arrive, after the quantization, at a generalized Wheeler-DeWitt equation for a wave functional that depends on the 4-metric of spacetime, the matter coordinates, and $τ$. Such generalized theory resolves some well known problems of quantum gravity, including "the problem of time".

math-ph↗

arXiv2014

On the quantisation of gravity by embedding spacetime in a higher dimensional space

Certain difficulties of quantum gravity can be avoided if we embed the spacetime $V_4$ into a higher dimensional space $V_N$; then our spacetime is merely a 4-surface in $V_N$.What remains is conceptually not so difficult: just to quantise this 4-surface. Our formal procedure generalises our version of Stueckelberg's proper time method of worldline quantisation. We write the equations of $V_4$ in the covariant canonical form starting from a model Lagrangian which contains the classical Einstein gravity as a particular case. Then we perform quantisation in the Schrödinger picture by using the concepts of a phase functional and wave functional. As a result we obtain the uncertainty relations which imply that an observer is `aware' either of a particular spacetime surface and has no information about other spacetime surfaces (which represent alternative histories); or conversely, he loses information about a particular $V_4$ whilst he obtains some information about other spacetimes (and histories). Equivalently, one cannot measure to an arbitrary precision both the metric on $V_4$ and matter distribution on various alternative spacetime surfaces. We show how this special case in the `coordinate' representations can be generalised to an arbitrary vector in an abstract Hilbert space.

gr-qc↗

arXiv2013

Stable Self-Interacting Pais-Uhlenbeck Oscillator

It is shown that the interacting Pais-Uhlenbeck oscillator necessarily leads to a description with a Hamiltonian that contains positive and negative energies associated with two oscillators. Descriptions with a positive definite Hamiltonians, considered by some authors, can hold only for a free Pais-Uhlenbeck oscillator. We demonstrate that the solutions of a self-interacting Pais-Uhlenbeck oscillator are stable on islands in the parameter space, as already observed in the literature. If we slightly modify the system, by considering a sine interaction term, and/or by taking unequal masses of the two oscillators, then the system is stable on the continents that extend from zero to infinity in the parameter space. Therefore, the Pais-Uhlenbeck oscillator is quite acceptable physical system.

gr-qc↗

arXiv2013

Geometric Spinors, Generalized Dirac Equation and Mirror Particles

It is shown that since the geometric spinors are elements of Clifford algebras, they must have the same transformation properties as any other Clifford number. In general, a Clifford number $Φ$ transforms into a new Clifford number $Φ'$ according to $Φ\to Φ' = {\rm{R}}\,Φ\,{\rm{S}}$, i.e., by the multiplication from the left and from the right by two Clifford numbers ${\rm R}$ and ${\rm S}$. We study the case of $Cl(1,3)$, which is the Clifford algebra of the Minkowski spacetime. Depending on choice of ${\rm R}$ and ${\rm S}$, there are various possibilities, including the transformations of vectors into 3-vectors, and the transformations of the spinors of one minimal left ideal of $Cl(1,3)$ into another minimal left ideal. This, among others, has implications for understanding the observed non-conservation of parity.

hep-th↗