Stochastic Mechanics and the Unification of Quantum Mechanics with Brownian Motion

We unify Brownian motion and quantum mechanics in a single mathematical framework. In particular, we show that non-relativistic quantum mechanics of a single spinless particle on a flat space can be described by a Wiener process that is rotated in the complex plane. We then extend this theory to relativistic stochastic theories on manifolds using the framework of second order geometry. As a byproduct, our results suggest that a consistent path integral based formulation of a quantum theory on a Lorentzian (Riemannian) manifold requires an Ito deformation of the Poincare (Galilean) symmetry, arising due to the coupling of the quadratic variation to the affine connection.Comment: 113 pages; preprint of a book published by Springer Natur

Quantum Mechanics from Stochastic Processes

We construct an explicit one-to-one correspondence between non-relativistic stochastic processes and solutions of the Schrodinger equation and between relativistic stochastic processes and solutions of the Klein-Gordon equation. The existence of this equivalence suggests that the Lorentzian path integral can be defined as an Ito integral, similar to the definition of the Euclidean path integral in terms of the Wiener integral. Moreover, the result implies a stochastic interpretation of quantum theories.Comment: 9 page

Bounds on very weakly interacting ultra light scalar and pseudoscalar dark matter from quantum gravity

In this paper we consider very weakly interacting and ultra light scalar and pseudoscalar dark matter candidates. We show that quantum gravity has important implications for such models and that the masses of the singlet scalar and pseudoscalar fields must be heavier than 3×10−3 eV. However, if they are gauged, their masses could be much lighter and as light as 10−22eV. The existence of new gauge forces in the dark matter sector can thus be probed by atomic clocks or quantum sensors experiments

Analytic continuation of stochastic mechanics

We study a (relativistic) Wiener process on a complexified (pseudo-)Riemannian manifold. Using Nelson’s stochastic quantization procedure, we derive three equivalent descriptions for this problem. If the process has a purely real quadratic variation, we obtain the one-sided Wiener process that is encountered in the theory of Brownian motion. In this case, the result coincides with the Feyman–Kac formula. On the other hand, for a purely imaginary quadratic variation, we obtain the two-sided Wiener process that is encountered in stochastic mechanics, which provides a stochastic description of a quantum particle on a curved spacetim

Stochastic quantization on Lorentzian manifolds

We embed Nelson’s theory of stochastic quantization in the Schwartz-Meyer second order geometry framework. The result is a non-perturbative theory of quantum mechanics on (pseudo-)Riemannian manifolds. Within this approach, we derive stochastic differential equations for massive spin-0 test particles charged under scalar potentials, vector potentials and gravity. Furthermore, we derive the associated Schrödinger equation. The resulting equations show that massive scalar particles must be conformally coupled to gravity in a theory of quantum gravity. We conclude with a discussion of some prospects of the stochastic framework

The road to quantum gravity: from elementary considerations to universal predictions

General relativity and quantum theory are two cornerstones of modern physics, which, despite their huge individual successes, have so far failed to work together in a complete and consistent way. As a consequence, the unification of the two theories in a consistent formulation of quantum field theory on curved spacetimes and eventually in a theory of quantum gravity has become one of the holy grails of modern physics. In this thesis, some of the many aspects of such a theory of quantum gravity are explored. The first part of the thesis is devoted to the construction of diffeomorphism invariant theories on a spacetime that is itself uctuating. We show how this can be achieved for basic theories using second order geometry, which is an extension of the geometrical framework applied in general relativity. After these elementary considerations, we move on to study predictions from quantum gravity at sub-Planckian energy scales, where quantum field theory and general relativity can be combined in the framework of effective field theory. The resulting effective field theory of gravity allows to make model independent predictions in quantum gravity. In the second part of the thesis, we discuss perturbative predictions following from the unique effective action for quantum gravity. Here, we particularly focus on predictions from this formalism for compact stars, black holes and the fate of singularities in quantum gravity. Finally, in the third part, we use effective field theory and the universality of the gravitational coupling to study quantum gravitational effects that lie within the reach of current experiments. We then discuss the implications for beyond the Standard Model physics and dark matter models in particular

Emerging roles of bile acids in control of intestinal functions

PURPOSE OF REVIEW: Bile acids and their signalling pathways are increasingly recognized as potential therapeutic targets for several diseases. This review summarizes new insights in bile acid physiology, focussing on regulatory roles of bile acids in intestinal functions. RECENT FINDINGS: Recent studies have highlighted the interactions between bile acids and gut microbiome: interfering with microbiome composition may be beneficial in treatment of liver and metabolic diseases by modulating bile acid composition, as different bile acid species have different signalling functions. In the intestine, bile acid receptors FXR, VDR and TGR5 are involved in control of barrier function, paracellular ion transport and hormone release. Specific microbial bile acid metabolites modulate immune responses of the host. In addition, new functions of bile acids in regulation of gastric emptying and satiation via brain-gut-liver axis have been discovered. Identification of Cyp2c70 as the enzyme responsible for generation of hydrophilic mouse/rat-specific muricholic acids has allowed the generation of murine models with a human-like bile acid composition. SUMMARY: Specific bile acids act as important signalling molecules affecting whole body metabolism, specific transport processes and immunity in different segments of the intestinal tract. Their relevance for human (patho)physiology is emerging. Novel mouse models with human-like bile acid composition will aid to accelerate translational research

Quantum corrected equations of motion in the interior and exterior Schwarzschild spacetimes

In this paper we derive the leading quantum gravitational corrections to the geodesics and the equations of motion for a scalar field in the spacetime containing a constant density star. It is shown that these corrections can be calculated in quantum gravity reliably and in a model independent way. Furthermore, we find that quantum gravity gives rise to an additional redshift that results from the gradient instead of the amplitude of the density profile

Role of bile acids in inflammatory liver diseases

Bile acids and their signaling pathways are increasingly recognized as potential therapeutic targets for cholestatic and metabolic liver diseases. This review summarizes new insights in bile acid physiology, focusing on regulatory roles of bile acids in the control of immune regulation and on effects of pharmacological modulators of bile acid signaling pathways in human liver disease. Recent mouse studies have highlighted the importance of the interactions between bile acids and gut microbiome. Interfering with microbiome composition may be beneficial for cholestatic and metabolic liver diseases by modulating formation of secondary bile acids, as different bile acid species have different signaling functions. Bile acid receptors such as FXR, VDR, and TGR5 are expressed in a variety of cells involved in innate as well as adaptive immunity, and specific microbial bile acid metabolites positively modulate immune responses of the host. Identification of Cyp2c70 as the enzyme responsible for the generation of hydrophilic mouse/rat-specific muricholic acids has allowed the generation of murine models with a human-like bile acid composition. These novel mouse models will aid to accelerate translational research on the (patho)physiological roles of bile acids in human liver diseases