In this paper we will define a Lagrangian for scalar and gauge fields on causal sets, based on the selection of an Alexandrov set in which the variations of appropriate expressions in terms of either the scalar field or the gauge field holonomies aro
und suitable loops take on the least value. For these fields, we will find that the values of the variations of these expressions define Lagrangians in covariant form.
The goal of this paper is to re-express QFT in terms of two classical fields living in ordinary space with single extra dimension. The role of the first classical field is to set up an injection from the set of values of extra dimension into the set
of functions, and then said injection will be used in order to convert the second field into a coarse grained functional, thereby approximating QFT state. It turns out that this work also has a side-benefit of modeling ensemble of states in terms of one single state which, in turn, is interpretted in the above way. It is important to clarify that by classical we mean functions over ordinary space rather than configuration, Fock or function space. The classical theory that we propose is still non-local.
It is commonly assumed that zero and non-zero photon mass would lead to qualitatively different physics. For example, massless photon has two polarization degrees of freedom, while massive photon at least three. This feature seems counter-intuitive.
In this paper we will show that if we change propagator by setting $i epsilon$ (needed to avoid poles) to a finite value, and also introduce it in a way that breaks Lawrentz symmetry, then we would obtain the continuous transition we desire once the speed of the photons is large enough with respect to preferred frame. The two transverse polarization degrees of freedom will be long lived, while longitudinal will be short lived. Their lifetime will be near-zero if $m ll sqrt{epsilon}$, which is where the properties of two circular polarizations arize. The $i epsilon$ corresponds to the intensity of Menskys continuous measurement and the short lifetime of the longitudinal photons can be understood as the conversion of quantum degrees of freedom (photons) into classical ones by the measurement device (thus getting rid of the former). While the classical trajectory of the longitudinal photons does arize, it plays no physical role due to quantum Zeno effect: intuitively, it is similar to an electron being kept at a ground state due to continuous measurement.
Mensky has suggested to account for continuous measurement by attaching to a path integral a weight function centered around the classical path that the integral assigns a probability amplitude to. We show that in fact this weight function doesnt hav
e to be viewed as an additional ingredient put in by hand. It can be derived instead from the conventional path integral if the infinitesimal term iepsilon in the propagator is made finite; the classical trajectory is proportional to the current.
In this paper we will show how Menskys model of restricted path integrals can be derived from GRW spontaneous collapse model.
In this paper we will utilize the non-trivial shapes of the strings in order to come up with realistic definition of probability amplitudes in a lot more natural way than could be done in point particle counterpart. We then go on to translate GRW mod
el to string theory context. In this paper we limit ourselves to boson-only toy model without D-branes.
The goal of this paper is to define the Grassmann integral in terms of a limit of a sum around a well-defined contour so that Grassmann numbers gain geometric meaning rather than symbols. The unusual rescaling properties of the integration of an expo
nential is due to the fact that the integral attains the known values only over a specific set of contours and not over their rescale
A while ago a proposal have been made regarding Klein Gordon and Maxwell Lagrangians for causal set theory. These Lagrangian densities are based on the statistical analysis of the behavior of field on a sample of points taken throughout some small re
gion of spacetime. However, in order for that sample to be statistically reliable, a lower bound on the size of that region needs to be imposed. This results in unwanted contributions from higher order derivatives to the Lagrangian density, as well as non-trivial curvature effects on the latter. It turns out that both gravitational and non-gravitational effects end up being highly non-linear. In the previous papers we were focused on leading order terms, which allowed us to neglect these nonlinearities. We would now like to go to the next order and investigate them. In the current paper we will exclusively focus on the effects of higher order derivatives in the flat-space toy model. The gravitational effects will be studied in another paper which is currently in preparation. Both papers are restricted to bosonic fields, although the issue probably generalizes to fermions once Grassmann numbers are dealt with in appropriate manner.
The purpose of this paper is to propose a classical model of quantum fields which is local. Yet it admittedly violates relativity as we know it and, instead, it fits within a bimetric model with one metric corresponding to speed of light and another
metric to superlumianl signals whose speed is still finite albeit very large. The key obstacle to such model is the notion of functional in the context of QFT which is inherently non-local. The goal of this paper is to stop viewing functionals as fundamental and instead model their emergence from the deeper processes that are based on functions over $mathbb{R}^4$ alone. The latter are claimed to be local in the above bimetric sense.
This paper has few different, but interrelated, goals. At first, we will propose a version of discretization of quantum field theory (Chapter 3). We will write down Lagrangians for sample bosonic fields (Section 3.1) and also attempt to generalize th
em to fermionic QFT (Section 3.2). At the same time, we will insist that the elements of our discrete space are embedded into a continuum. This will allow us to embed several different lattices into the same continuum and view them as separate quantum field configurations. Classical parameters will be used in order to specify which lattice each given element belongs to. Furthermore, another set of classical parameters will be proposed in order to define so-called probability amplitude of each field configuration, embodied by a corresponding lattice, taking place (Chapter 2). Apart from that, we will propose a set of classical signals that propagate throughout continuum, and define their dynamics in such a way that they produce the mathematical information consistent with the desired quantum effects within the lattices we are concerned about (Chapter 4). Finally, we will take advantage of the lack of true quantum mechanics, and add gravity in such a way that avoids the issue of its quantization altogether (Chapter 5). In the process of doing so, we will propose a gravity-based collapse model of a wave function. In particular, we will claim that the collapse of a wave function is merely a result of states that violate Einsteins equation being thrown away. The mathematical structure of this model (in particular, the appeal to gamblers ruin) will be similar to GRW collapse models.
