Introduction to Lattice Field Theory
... The result looks trivial because the hard task of diagonalizing the
Hamiltonian is already done. In any other basis the path integral is
By choosing position eigenstates as the basis, Feynman  showed
that the infinitesimal evolution operator for a single particle is
hx| U(0, ...
Entanglement Entropy of non-Unitary Quantum Field Theory
... system is critical and we expect to be able to extract the
central charge c of the critical point.
What happens if |ψi is the ground state of a critical system
described by a non-unitary CFT? We find that we may just
replace c → ceff = c − 24∆.
Here ceff is the effective central charge and ∆ is the
Dirac Operators on Noncommutative Spacetimes ?
... as a natural generalization of ordinary differential geometry. It is also of crucial interest from
a physical perspective, since it generically plays a role when the principles of quantum mechanics
are combined with those of general relativity [17, 18]. In both contexts, Dirac operators are of
Lectures on Conformal Field Theory arXiv:1511.04074v2 [hep
... transformations. What other transformations should we consider? We will begin with
the most intuitive conformal transformation: a scale transformation (as in Figure
1). Scale transformations act by rescaling, or zooming in and out of some region
of spacetime. If we split the space and time coordinat ...
String Theory. Volume 1, Introduction to the Bosonic String
... From the beginning it was clear that, despite its successes, the Standard Model of elementary particles would have to be embedded in a
broader theory that would incorporate gravitation as well as the strong and
electroweak interactions. There is at present only one plausible candidate
for such a the ...
Factorization algebras and free field theories
... my time there a pleasure. David Nadler has profoundly shaped my approach to and perspective
on mathematics, starting with his guidance of the wonderful explorations I undertook with Mike
and Ian that first year and continuing on in his demanding but rewarding seminar, and through
numerous conversati ...
Light-Front Holographic QCD and Emerging
... ground-state configurations and the unavoidable presence of multi-hadron thresholds .
Furthermore, dynamical observables in Minkowski space-time are not obtained directly
from Euclidean space lattice computations. Other methods, as for example the DysonSchwinger equations, have also led to many i ...
Phenomenology of Higgs Bosons Beyond the Standard Model
... where i = 1, 2, 3 is the color index of the quark. The terms inside the large
parenthesis in (2.11) make up the covariant derivative Dμi j , and Aaμ are the
gauge ﬁelds which are called gluons and there are 8 of them. This theory,
where the ﬁelds Ψi are transformed into a linear combination of thems ...
How long does it take until a quantum system
... the initial state were precisely known, it would be impossible to predict with certainty
what the final quantum state will be. Moreover, the pure initial state has zero entropy,
but at the end, according to Hawking, its entropy is of the order of m
2 , where M is the
total mass of the system a ...
- Free Documents
... of work that followed, it became clear that a useful framework for under
standing this situation is Atiyahs axiomatic description of a topological
quantum eld theory, or TQFT.
On the other hand, at about the same time as Jones initial discov
ery, Ashtekar discovered a reformulation of general relati ...
The Asymptotic Safety Scenario in Quantum Gravity
... quantum degrees of freedom. Second, a physics premise (“antiscreening”) is made about the selfinteraction of these quantum degrees of freedom in the ultraviolet. Third, the effective diminution
of the relevant degrees of freedom in the ultraviolet (on which morally speaking all approaches
agree) is ...
15. GRAND UNIFIED THEORIES 15. Grand Uniﬁed Theories 15.1. Grand Uniﬁcation 1
... 15.1.3. String Theory and Orbifold GUTs :
Orbifold compactiﬁcation of the heterotic string [7–9], and recent ﬁeld theoretic
constructions known as orbifold GUTs , contain grand uniﬁed symmetries realized in
5 and 6 dimensions. However, upon compactifying all but four of these extra dimensions,
Gauge and Matter Fields on a Lattice - Generalizing
... not be distinguished by te usual Ginzburg-Landau scheme of symmetry breaking. Therefore, a new mathematical framework for the study of such phases
is needed. In this dissertation we present the simplest example of a topologically ordered system, namely, the Toric Code (TC) introduced by A. Kitaev
Theoretical and observational consistency of Massive Gravity
... categories of the theoretical proposals for dark energy that have been
considered in the literature and very soon concentrate on massive
gravity as an alternative to dark energy in chapter 2. We will discuss
the recently developed ghost-free nonlinear theory for massive spin2 fields, the de Rham-Gab ...
Preparing topologically ordered states by Hamiltonian
... To use topologically ordered systems as quantum memories and for fault-tolerant quantum
computation, concrete procedures for the preparation of specific ground states are required.
Such mechanisms depend on the model Hamiltonian which is being realized as well as on the
particular experimental reali ...
Towards the mathematics of quantum field theory
... The notion of field is very general. From the mathematician’s viewpoint, it means a
x : M −→ C
between two spaces, that represents the motion of a physical object in a configuration
space C, with parameter space M . The notion of space must be taken here in a widely
generalized sense, becau ...
Ecole Doctorale de Physique et de Chimie Physique
... helps in addressing several other unresolved issues in the Standard Model framework. Only focusing on the lightest charginos and neutralinos decaying into one or more light leptons, we have
shown in our study that these models can be easily discovered in multi-leptonic final states as they
lead to s ...
In theoretical physics, BRST quantization (where the BRST refers to Becchi, Rouet, Stora and Tyutin) denotes a relatively rigorous mathematical approach to quantizing a field theory with a gauge symmetry. Quantization rules in earlier QFT frameworks resembled ""prescriptions"" or ""heuristics"" more than proofs, especially in non-abelian QFT, where the use of ""ghost fields"" with superficially bizarre properties is almost unavoidable for technical reasons related to renormalization and anomaly cancellation. The BRST global supersymmetry introduced in the mid-1970s was quickly understood to rationalize the introduction of these Faddeev–Popov ghosts and their exclusion from ""physical"" asymptotic states when performing QFT calculations. Crucially, this symmetry of the path integral is preserved in loop order, and thus prevents introduction of counterterms which might spoil renormalizability of gauge theories. Work by other authors a few years later related the BRST operator to the existence of a rigorous alternative to path integrals when quantizing a gauge theory.Only in the late 1980s, when QFT was reformulated in fiber bundle language for application to problems in the topology of low-dimensional manifolds, did it become apparent that the BRST ""transformation"" is fundamentally geometrical in character. In this light, ""BRST quantization"" becomes more than an alternate way to arrive at anomaly-cancelling ghosts. It is a different perspective on what the ghost fields represent, why the Faddeev–Popov method works, and how it is related to the use of Hamiltonian mechanics to construct a perturbative framework. The relationship between gauge invariance and ""BRST invariance"" forces the choice of a Hamiltonian system whose states are composed of ""particles"" according to the rules familiar from the canonical quantization formalism. This esoteric consistency condition therefore comes quite close to explaining how quanta and fermions arise in physics to begin with.In certain cases, notably gravity and supergravity, BRST must be superseded by a more general formalism, the Batalin–Vilkovisky formalism.