A unified geometric framework for boundary charges and dressings: non-Abelian theory and matter

Boundaries in gauge theories are a delicate issue. Arbitrary boundary choices enter the calculation of charges via Noether's second theorem, obstructing the assignment of unambiguous physical charges to local gauge symmetries. Replacing the arbitrary boundary choice with new degrees of freedom suggests itself. But, concretely, such boundary degrees of freedom are spurious---i.e. they are not part of the original field content of the theory---and have to disappear upon gluing. How should we fit them into what we know about field-theory? We resolve these issues in a unified and geometric manner, by introducing a connection 1-form, $\varpi$, in the field-space of Yang-Mills theory. Using this geometric tool, a modified version of symplectic geometry---here called `horizontal'---is possible. Independently of boundary conditions, this formalism bestows to each region a physical notion of charge: the horizontal Noether charge. The horizontal gauge charges always vanish, while global charges still arise for reducible configurations characterized by global symmetries. The field-content itself is used as a reference frame to distinguish `gauge' and `physical'; no new degrees of freedom, such as group-valued edge modes, are required. Different choices of reference fields give different $\varpi$'s, which are cousins of gauge-fixing like the Higgs-unitary and Coulomb gauges. But the formalism extends well beyond gauge-fixings, for instance by avoiding the Gribov problem. For one choice of $\varpi$, would-be Goldstone modes arising from the condensation of matter degrees of freedom play precisely the role of the known group-valued edge modes, but here they arise as preferred coordinates in field space, rather than new fields. For another choice, in the Abelian case, $\varpi$ recovers the Dirac dressing of the electron.Comment: 71 pages, 3 appendices, 9 figures. Summary of the results at the beginning of the paper. v2: numerous improvements in the presentation, and introduction of new references, taking colleague feedback into accoun

Foundations of Quantum Gravity : The Role of Principles Grounded in Empirical Reality

When attempting to assess the strengths and weaknesses of various principles in their potential role of guiding the formulation of a theory of quantum gravity, it is crucial to distinguish between principles which are strongly supported by empirical data - either directly or indirectly - and principles which instead (merely) rely heavily on theoretical arguments for their justification. These remarks are illustrated in terms of the current standard models of cosmology and particle physics, as well as their respective underlying theories, viz. general relativity and quantum (field) theory. It is argued that if history is to be of any guidance, the best chance to obtain the key structural features of a putative quantum gravity theory is by deducing them, in some form, from the appropriate empirical principles (analogous to the manner in which, say, the idea that gravitation is a curved spacetime phenomenon is arguably implied by the equivalence principle). It is subsequently argued that the appropriate empirical principles for quantum gravity should at least include (i) quantum nonlocality, (ii) irreducible indeterminacy, (iii) the thermodynamic arrow of time, (iv) homogeneity and isotropy of the observable universe on the largest scales. In each case, it is explained - when appropriate - how the principle in question could be implemented mathematically in a theory of quantum gravity, why it is considered to be of fundamental significance and also why contemporary accounts of it are insufficient.Comment: 21 pages. Some (mostly minor) corrections. Final published versio

What is Time? A New Mathematico- Physical and Information Theoretic Approach

A New Mathematico-Physical and Information Theoretic Approach Examination of the available hard core information to firm up the process of unification of quantum and gravitational physics leads to the conclusion that for achieving this synthesis, major paradigm shifts are needed as also the answering of `What is Time?' The object of this submission is to point out the means of achieving such a grand synthesis. Currently the main pillars supporting the edifice of physics are: (i) The geometrical concepts of space- time-gravitation, (ii) The dynamic concepts involving quantum of action, (iii) Statistical thermodynamic concepts, heat and entropy, (iv) Mathematical concepts, tools and techniques serving both as a grand plan and the means of calculation and last but not least v)Controlled observation, pertinent experimentation as the final arbiter. In making major changes the author is following Dirac's dictum "....make changes without sacrificing the existing superstructure". It is shown that time can be treated as a parameter rather than an additional dimension. A new entity called "Ekon" having the properties of both space and momentum is introduced along with a space called "Chalachala". The requisite connection with Einstein's formulation and mathematical aperatus required have been formulated which is highly suited for the purpose. The primacy of the Plancks quantum of action and its representation geometrically as a twist is introduced. The practical and numerical estimates have been made and applied to evaluation of the gravitational constant in a a seperate submission "Estimations of gravitational constant from CMBR data".Comment: 29 pages, pdf fil

Two Notions of Naturalness

My aim in this paper is twofold: (i) to distinguish two notions of naturalness employed in BSM physics and (ii) to argue that recognizing this distinction has methodological consequences. One notion of naturalness is an "autonomy of scales" requirement: it prohibits sensitive dependence of an effective field theory's low-energy observables on precise specification of the theory's description of cutoff-scale physics. I will argue that considerations from the general structure of effective field theory provide justification for the role this notion of naturalness has played in BSM model construction. A second, distinct notion construes naturalness as a statistical principle requiring that the values of the parameters in an effective field theory be "likely" given some appropriately chosen measure on some appropriately circumscribed space of models. I argue that these two notions are historically and conceptually related but are motivated by distinct theoretical considerations and admit of distinct kinds of solution.Comment: 34 pages, 1 figur