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Matej Pavsic

Publications and source records attributed to Matej Pavsic.

32 records · Page 2Linked to original sources
arXiv2003

Clifford Space as the Arena for Physics

A new theory is considered according to which extended objects in $n$-dimensional space are described in terms of multivector coordinates which are interpreted as generalizing the concept of centre of mass coordinates. While the usual centre of mass is a point, by generalizing the latter concept, we associate with every extended object a set of $r$-loops, $r=0,1,..., n-1$, enclosing oriented $(r+1)$-dimensional surfaces represented by Clifford numbers called $(r+1)$-vectors or multivectors. Superpositions of multivectors are called polyvectors or Clifford aggregates and they are elements of Clifford algebra. The set of all possible polyvectors forms a manifold, called $C$-space. We assume that the arena in which physics takes place is in fact not Minkowski space, but $C$-space. This has many far reaching physical implications, some of which are discussed in this paper. The most notable is the finding that although we start from the constrained relativity in $C$-space we arrive at the unconstrained Stueckelberg relativistic dynamics in Minkowski space which is a subspace of $C$-space.

gr-qc↗
arXiv2002

Clifford Algebra, Geometry and Physics

The geometric calculus based on Clifford algebra is a very useful tool for geometry and physics. It describes a geometric structure which is much richer than the ordinary geometry of spacetime. A Clifford manifold (C-space) consists not only of points, but also of 1-loops, 2-loops, etc.. They are associated with multivectors which are the wedge product of the basis vectors, the generators of Clifford algebra. Within C-space we can perform the so called polydimensional rotations which reshuffle the multivectors, e.g., a bivector into a vector, etc.. A consequence of such a polydimensional rotation is that the signature can change: it is relative to a chosen set of basis vectors. Another important consequence is that the well known unconstrained Stueckelberg theory is embedded within the constrained theory based on C-space. The essence of the Stueckelberg theory is the existence of an evolution parameter which is invariant under the Lorentz transformations. The latter parameter is interpreted as being the true time - associated with our perception of the passage of time.

gr-qc↗
arXiv2002

Spin and Electron Structure

The recent literature shows a renewed interest, with various independent approaches, in the classical models for spin. Considering the possible interest of those results, at least for the electron case, we purpose in this paper to explore their physical and mathematical meaning, by the natural and powerful language of Clifford algebras (which, incidentally, will allow us to unify those different approaches). In such models, the ordinary electron is in general associated to the mean motion of a point--like "constituent" Q, whose trajectory is a cylindrical helix. We find, in particular, that the object Q obeys a new, non-linear Dirac--like equation, such that --when averaging over an internal cycle (which corresponds to a linearization)-- it transforms into the ordinary Dirac equation (valid, of course, for the electron as a whole).

quant-ph↗
arXiv2001

External Inversion, Internal Inversion, and Reflection Invariance

Having in mind that physical systems have different levels of structure we develop the concept of external, internal and total improper Lorentz transformation (space inversion and time reversal). A particle obtained from the ordinary one by the application of internal space inversion or time reversal is generally a different particle. From this point of view the intrinsic parity of a nuclear particle (`elementary particle') is in fact the external intrinsic parity, if we take into account the internal structure of a particle. We show that non-conservation of the external parity does not necessarily imply non-invariance of nature under space inversion. The conventional theory of beta-decay can be corrected by including the internal degrees of freedom to become invariant under total space inversion, though not under the external one.

hep-ph↗
arXiv2001

An Alternative to Matter Localization in the "Brane World": An Early Proposal and its Later Improvements

Here we place the Latex typeset of the paper M. Pavsic, Phys. Lett. A116 (1986) 1-5. In the paper we presented the picture that our spacetime is a 3-brane moving in a higher dimensional space. The dynamical equations were derived from the action which is just that for the usual Dirac-Nambu-Goto $p$-brane. We also considered the case where not only one, but many branes of various dimensionalities are present, and showed that their intersections with the 3-brane manifest as matter in 4-dimensional spacetime. We considered a particular case, where the intersections behaved as point particles, and found out that they follow the geodesics on the 3-brane worldsheet (identified with our spacetime). In a series of subsequent papers the original idea has been further improved and developped. This is discussed in a note at the end, where it is also pointed out that such a model resolves the problem of massive matter confinement on the brane, recently discussed by Rubakov et al. and Mueck et al.

gr-qc↗
arXiv2000

Clifford Algebra Based Polydimensional Relativity and Relativistic Dynamics

Starting from the geometric calculus based on Clifford algebra, the idea that physical quantities are Clifford aggregates ("polyvectors") is explored. A generalized point particle action ("polyvector action") is proposed. It is shown that the polyvector action, because of the presence of a scalar (more precisely a pseudoscalar) variable, can be reduced to the well known, unconstrained, Stueckelberg action which involves an invariant evolution parameter. It is pointed out that, starting from a different direction, DeWitt and Rovelli postulated the existence of a clock variable attached to particles which serve as a reference system for identification of spacetime points. The action they postulated is equivalent to the polyvector action. Relativistic dynamics (with an invariant evolution parameter) is thus shown to be based on even stronger theoretical and conceptual foundations than usually believed.

hep-th↗
arXiv2000

A Brane World Model with Intersecting Branes

A brane world model is investigated, in which there are many branes that may intersect and self intersect. One of the branes, being a 3-brane, represents our spacetime, while the other branes, if they intersect our brane world, manifest themselves as matter in our 3-brane. It is shown that such a matter encompasses dust of point particles and higher dimensional p-branes, and all those objects follow "geodesics" in the world volume swept by our 3-brane. We also point point out that such a model can be formulated in a background independent way, and that the kinetic term for gravity arises from quantum fluctuation of the brane.

hep-th↗
arXiv1998

Pseudo Euclidean-Signature Harmonic Oscillator, Quantum Field Theory and Vanishing Cosmological Constant

The harmonic oscillator in pseudo euclidean space is studied. A straightforward procedure reveals that although such a system may have negative energy, it is stable. In the quantized theory the vacuum state has to be suitably defined and then the zero-point energy corresponding to a positive-signature component is canceled by the one corresponding to a negative-signature component. This principle is then applied to a system of scalar fields. The metric in the space of fields is assumed to have signature (+ + + ... - - -) and it is shown that the vacuum energy, and consequently the cosmological constant, are then exactly zero. The theory also predicts the existence of stable, negative energy field excitations (the so called "exotic matter") which are sources of repulsive gravitational fields, necessary for construction of the time machines and Alcubierre's hyperfast warp drive.

hep-th↗
arXiv1997

The Dirac-Nambu-Goto p-Branes as Particular Solutions to a Generalized, Unconstrained Theory

The theory of the usual, constrained p-branes is embedded into a larger theory in which there is no constraints. In the latter theory the Fock-Schwinger proper time formalism is extended from point-particles to membranes of arbitrary dimension. For this purpose the tensor calculus in the infinite dimensional membrane space M is developed and an action which is covariant under reparametrizations in M is proposed. The canonical and Hamiltonian formalism is elaborated in detail. The quantization appears to be straightforward and elegant. No problem with unitarity arises. The conventional p-brane states are particular stationary solutions to the functional Schroedinger equation which describes the evolution of a membrane's state with respect to the invariant evolution parameter tau. A tau-dependent solution which corresponds to the wave packet of a null p-brane is found. It is also shown that states of a lower dimensional membrane can be considered as particular states of a higher dimensional membrane.

hep-th↗
arXiv1996

Fock-Schwinger proper time formalism for p-branes

The theory of the usual, constrained p-branes is embedded into a larger theory in which there is no constraints. In the latter theory the Fock-Schwinger proper time formalism is extended from point-particles to p-branes which can be considered as a points in an infinite dimensional space M. The quantization appears to be straightforward and elegant. The conventional p-brane states are particular stationary solutions to the functional Schrödinger equation which describes the evolution of a membrane's state with respect to the invariant evolution parameter $τ$. It is also shown that states of a lower dimensional p-brane can be considered as particular states of a higher dimensional p-brane.

hep-th↗
arXiv1995

The Embedding Model of Induced Gravity with Bosonic Sources

We consider a theory in which spacetime is an n-dimensional surface $V_n$ embedded in an $N$-dimensional space $V_N$. In order to enable also the Kaluza-Klein approach we admit $n > 4$. The dynamics is given by the minimal surface action in a curved embedding space. The latter is taken, in our specific model, as being a conformally flat space. In the quantization of the model we start from a generalization of the Howe-Tucker action which depends on the embedding variables $η^a (x)$ and the (intrinsic) induced metric $g_{μν}$ on $V_n$. If in the path integral we perform only the functional integration over $η^a (x)$, we obtain the effective action which functionally depends on $g_{μν}$ and contains the Ricci scalar $R$ and its higher orders $R^2$ etc. But due to our special choice of the conformal factor in $V_N$ enterig our original action, it turns out that the effective action contains also the source term. The latter is in general that of a $p$-dimensional membrane ($p$-brane); in particular we consider the case of a point particle. Thus, starting from the basic fields $η^a (x)$, we induce not only the kinetic term for $g_{μν}$, but also the "matter" source term.

gr-qc↗
arXiv1995

On the Resolution of Time Problem in Quantum Gravity Induced from Unconstrained Membranes

The relativistic theory of unconstrained $p$-dimensional membranes ($p$-branes) is further developed and then applied to the embedding model of induced gravity. Space-time is considered as a 4-dimensional unconstrained membrane evolving in an $N$-dimensional embedding space. The parameter of evolution or the evolution time $τ$ is a distinct concept from the coordinate time $t = x^0$. Quantization of the theory is also discussed. A covariant functional Schr\" odinger equations has a solution for the wave functional such that it is sharply localized in a certain subspace $P$ of space-time, and much less sharply localized (though still localized) outside $P$. With the passage of evolution the region $P$ moves forward in space-time. Such a solution we interpret as incorporating two seemingly contradictory observations: (i) experiments clearly indicate that space-time is a continuum in which events are existing; (ii) not the whole 4-dimensional space-time, but only a 3-dimensional section which moves forward in time is accessible to our immediate experience. The notorious problem of time is thus resolved in our approach to quantum gravity. Finally we include sources into our unconstrained embedding model. Possible sources are unconstrained worldlines which are free from the well known problem concerning the Maxwell fields generated by charged unconstrained point particles.

gr-qc↗
arXiv1995

The Classical and Quantum Theory of Relativistic p-Branes without Constraints

It is shown that a relativistic (i.e. a Poincar{\' e} invariant) theory of extended objects (called p-branes) is not necessarily invariant under reparametrizations of corresponding $p$-dimensional worldsheets (including worldlines for $p = 0$). Consequnetly, no constraints among the dynamical variables are necessary and quantization is straightforward. Additional degrees of freedom so obtained are given a physical interpretation as being related to membrane's elastic deformations ("wiggleness"). In particular, such a more general, unconstrained theory implies as solutions also those p-brane states that are solutions of the conventional theory of the Dirac-Nambu-Goto type.

gr-qc↗