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We present an integral formalism for constructing scheme transformations in a quantum field theory. We apply this to generate several new useful scheme transformations. A comparative analysis is given of these scheme transformations in…
It has been suggested that one may construct a Lorentz-invariant noncommutative field theory by extending the coordinate algebra to additional, fictitious coordinates that transform nontrivially under the Lorentz group. Integration over…
We consider scalar quantum fields on the sphere, both massive and massless. In the massive case we show that the correlation functions define amplitudes which are trace class operators between tensor products of a fixed Hilbert space. We…
We show that variants of the classical reflection functors from quiver representation theory exist in any abstract stable homotopy theory, making them available for example over arbitrary ground rings, for quasi-coherent modules on schemes,…
The canonical quantization of diffeomorphism invariant theories of connections in terms of loop variables is revisited. Such theories include general relativity described in terms of Ashtekar-Barbero variables and extension to Yang-Mills…
Scalar effective field theories with enhanced soft limits behave in many ways like gauge theories and gravity. In particular, symmetries fix the structure of interactions and the tree-level S-matrix in both types of theories. We explore how…
The effective field theory of inflation is a powerful tool for obtaining model independent predictions common to large classes of inflationary models. It requires only information about the symmetries broken during the inflationary era, and…
The well known Adler zero can fully determine tree amplitudes of non-linear sigma model (NLSM), but fails to fix tree pion amplitudes with higher-derivative interactions. To fill this gap, in this paper we propose a new method based on…
The Carroll algebra is constructed as the $c\to0$ limit of the Poincare algebra and is associated to symmetries on generic null surfaces. In this paper, we begin investigations of Carrollian fermions or fermions defined on generic null…
When studying gauge theories in the presence of boundaries, local symmetry transformations are typically classified as gauge or physical depending on whether the associated charges vanish or not. Here, we propose that physical charges…
In recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. We consider the quantum dynamics of a real massless scalar field coupled to…
This paper is concerned with the quantum theory of noncommutative scalar fields in two dimensional space time. It is shown that the noncommutativity originates from the the deformation of symplectic structures. The quantization is performed…
We derive a universal soft theorem for every scattering amplitude with at least one massless particle in an arbitrary theory of scalars. Our results follow from the geometry of field space and are valid for any choice of mass spectrum,…
We investigate the combinatorial properties of the functional equation $\phi[h(z)]=h(qz)$ for the conjugation of a formal diffeomorphism $\phi$ of $\mathbb{C}$ to its linear part $z\mapsto qz$. This is done by interpreting the functional…
By introducing auxiliary fields, which by their quantum numbers vanish in perturbation theory, we relate the dynamical perturbation theory of Pagels and Stokar and a successful gauged nonlocal constituent quark model to $U(N)$ gauge theory…
This paper investigates how tree-level amplitudes with massless quarks, gluons and/or massless scalars transforming under a single copy of the gauge group can be expressed in the context of the scattering equations as a sum over the…
We provide explicit formulas of non-recursive type for the linearizing transformations of a non-resonant analytic germ of diffeomorphism at a fixed point or a non-resonant analytic germ of vector field at a singular point, in any complex…
In this paper we start a systematic study of quantum field theory on random trees. Using precise probability estimates on their Galton-Watson branches and a multiscale analysis, we establish the general power counting of averaged Feynman…
Using the dilaton theorem, we show that the classical action of closed string field theory vanishes on-shell.
We develop the diffeomorphism invariant Colombeau-type algebra of nonlinear generalized functions in a modern and compact way. Using a unifying formalism for the local setting and on manifolds, the construction becomes simpler and more…