Dynamical Field Inference and Supersymmetry

Knowledge on evolving physical fields is of paramount importance in science, technology, and economics. Dynamical field inference (DFI) addresses the problem of reconstructing a stochastically-driven, dynamically-evolving field from finite data. It relies on information field theory (IFT), the information theory for fields. Here, the relations of DFI, IFT, and the recently developed supersymmetric theory of stochastics (STS) are established in a pedagogical discussion. In IFT, field expectation values can be calculated from the partition function of the full space-time inference problem. The partition function of the inference problem invokes a functional Dirac function to guarantee the dynamics, as well as a field-dependent functional determinant, to establish proper normalization, both impeding the necessary evaluation of the path integral over all field configurations. STS replaces these problematic expressions via the introduction of fermionic ghost and bosonic Lagrange fields, respectively. The action of these fields has a supersymmetry, which means there exists an exchange operation between bosons and fermions that leaves the system invariant. In contrast to this, measurements of the dynamical fields do not adhere to this supersymmetry. The supersymmetry can also be broken spontaneously, in which case the system evolves chaotically. This affects the predictability of the system and thereby makes DFI more challenging. We investigate the interplay of measurement constraints with the non-linear chaotic dynamics of a simplified, illustrative system with the help of Feynman diagrams and show that the Fermionic corrections are essential to obtain the correct posterior statistics over system trajectories.

Gauge-field-induced torsion and cosmic inflation

In this paper, inflation in the framework of Einstein–Cartan theory is revisited. Einstein–Cartan theory is a natural extension of the General Relativity with nonvanishing torsion. The connection on Riemann–Cartan space–time is only compatible with the cosmological principal for a particular form of torsion. We also show this form to be compatible with gauge invariance principle for non-Abelian and Abelian gauge fields under a certain deviced coupling procedure. We adopt an Abelian gauge field in the form of “cosmic triad”. The dynamical field equations are obtained and shown to sustain cosmic inflation with a large number of e-folds. We emphasize that at the end of inflation, torsion vanishes and the theory of Einstein–Cartan reduces to the General Relativity with the usual FRW geometry.

Sterile neutrinos, black hole vacuum and holographic principle

We construct an effective field theory (EFT) model that describes matter field interactions with Schwarzschild mini-black-holes (SBH’s), treated as a scalar field, $$B_0(x)$$ B 0 ( x ) . Fermion interactions with SBH’s require a complex spurion field, $$\theta _{ij}$$ θ ij , which we interpret as the EFT description of “holographic information,” which is correlated with the SBH as a composite system. We consider Hawking’s virtual black hole vacuum (VBH) as a Higgs phase, $$\langle B_0 \rangle =V$$ ⟨ B 0 ⟩ = V . Integrating sterile neutrino loops, the information field $$\theta _{ij}$$ θ ij is promoted to a dynamical field, necessarily developing a tachyonic instability and acquiring a VEV of order the Planck scale. For N sterile neutrinos this breaks the vacuum to $$SU(N)\times U(1)/SO(N)$$ S U ( N ) × U ( 1 ) / S O ( N ) with N degenerate Majorana masses, and $$\frac{1}{2}N(N+1)$$ 1 2 N ( N + 1 ) Nambu-Goldstone neutrino-Majorons. The model suggests many scalars fields, corresponding to all fermion bilinears, may exist bound nonperturbatively by gravity.

Variable Planck’s Constant: Treated As A Dynamical Field And Path Integral

The constant ħ is elevated to a dynamical field, coupling to other fields, and itself, through the Lagrangian density derivative terms. The spatial and temporal dependence of ħ falls directly out of the field equations themselves. Three solutions are found: a free field with a tadpole term; a standing-wave non-propagating mode; a non-oscillating non-propagating mode. The first two could be quantized. The third corresponds to a zero-momentum classical field that naturally decays spatially to a constant with no ad-hoc terms added to the Lagrangian. An attempt is made to calibrate the constants in the third solution based on experimental data. The three fields are referred to as actons. It is tentatively concluded that the acton origin coincides with a massive body, or point of infinite density, though is not mass dependent. An expression for the positional dependence of Planck’s constant is derived from a field theory in this work that matches in functional form that of one derived from considerations of Local Position Invariance violation in GR in another paper by this author. Astrophysical and Cosmological interpretations are provided. A derivation is shown for how the integrand in the path integral exponent becomes Lc/ħ(r), where Lc is the classical action. The path that makes stationary the integral in the exponent is termed the “dominant” path, and deviates from the classical path systematically due to the position dependence of ħ. The meaning of variable ħ is seen to be related to the rate of time passage along each path increment. The changes resulting in the Euler-Lagrange equation, Newton’s first and second laws, Newtonian gravity, Friedmann equation with a Cosmological Constant, and the impact on gravitational radiation for the dominant path are shown and discussed.

Dynamical instantons and activated processes in mean-field glass models

We focus on the energy landscape of a simple mean-field model of glasses and analyze activated barrier-crossing by combining the Kac-Rice method for high-dimensional Gaussian landscapes with dynamical field theory. In particular, we consider Langevin dynamics at low temperature in the energy landscape of the pure spherical p-spin model. We select as initial condition for the dynamics one of the many unstable index-1 saddles in the vicinity of a reference local minimum. We show that the associated dynamical mean-field equations admit two solutions: one corresponds to falling back to the original reference minimum, and the other to reaching a new minimum past the barrier. By varying the saddle we scan and characterize the properties of such minima reachable by activated barrier-crossing. Finally, using time-reversal transformations, we construct the two-point function dynamical instanton of the corresponding activated process.

Gauge Field Theory and Gravitation

The notion of 2-spinor soldering form allows a neat formulation, called the ‘tetrad-affine setting’, of a theory of matter and gauge fields interacting with the gravitational field. The latter is represented by a couple constituted by the soldering form and a 2-spinor connection. This approach is suited to describe matter fields with arbitrary spin and generic further internal structure. In particular one gets an approach to interacting Einstein-Cartan-Maxwell-Dirac fields, in which the only assumption is a complex bundle with 2-dimensional fibers: the needed bundles are obtained from it by natural geometric contructions, and any object which is not determined from these ‘minimal geometric data’ is assumed to be a dynamical field.

Numerical assessment of the mixed convection and volumetric radiation in a vertical channel with MRT-LBM

Purpose The paper aims to focus on modeling of combined mixed convection and volumetric radiation within a vertical channel using a hybrid thermal lattice Boltzmann method (LBM). The multiple relaxation time LBM (MRT-LBM) is used to compute the dynamical field. The thermal field is determined by a finite difference method (FDM), and the simple relaxation time-LBM (SRT-LBM) serves to calculate the radiative part. The geometry considered concerns a vertical channel defined by two diffuse and isothermal walls. The active fluid represents a gray gas participating in absorption, emission and isotropically scattering. The parametrical study conducted aims to highlight the effect of Richardson number (Ri), Planck number (Pl) and the optical thickness (τ) on dynamical and thermal fields. It is found that radiation affects greatly heat transfer. Design/methodology/approach MRT-LBM is used to compute the dynamical field. The thermal field is determined by FDM, and SRT-LBM serves to calculate the radiative part. Findings This study has shown the strong capability of this approach to simulate similar problems. The Planck number largely affects the streamlines and isotherms distribution. Also, it causes disappearance of reversal flow, undesirable in most industrial applications, for low Planck numbers. The optical thickness causes the disappearance of reversal flow, in the case in which it appears, for lower opacity. However, for higher opacity it leads to a recurrence of reversed flow. Originality/value The use of a new original method composed of MRT-LBM to solve the fluid velocity, FDM to handle the temperature equation and extended SRT-LBM to compute the radiative part of the energy equation.

Cosmological implications of Nambu–Jona-Lasinio model with a dynamical coupling

We study the cosmological implications of the Nambu–Jona-Lasinio (NJL) model when the coupling constant is field dependent. The NJL model has a four-fermion interaction describing two different phases due to quantum interaction effects and determined by the strength of the coupling constant [Formula: see text]. It describes massless fermions for weak coupling and a massive fermions and strong coupling, where a fermion condensate is formed. In the original NJL model, the coupling constant [Formula: see text] is indeed constant, and in this work we consider a modified version of the NJL model by introducing a dynamical field dependent coupling motivated by string theory. The effective potential as a function of the varying coupling (aimed to implement a natural phase transition) is seen to develop a negative divergence, i.e. becomes a “bottomless well” in certain limit region. Although we explain how an lower unbounded potential is not necessarily unacceptable in a cosmological context, the divergence can be removed if we consider a mass term for the coupling like field. We found that for a proper set of parameters, the total potential obtained has two minima, one located at the origin (the trivial solution, in which the fluid associated with the fields behave like matter); and the other related to the nontrivial solution. This last solution has three possibilities: (1) if the minimum is positive [Formula: see text], the system behaves as a cosmological constant, thus leading eventually to an accelerated universe; (2) if the minimized potential vanishes [Formula: see text], then we have matter with no acceleration; (3) finally a negative minimum [Formula: see text] leads an eventually collapsing universe with a flat geometry. Therefore, a possible interpretation as dark matter (DM) or dark energy (DE) is allowed among the behaviors implicated in the model.