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Modern perspectives in lattice QCD : quantum field theory and high performance computing
\"The book is based on the lectures delivered at the XCIII Session of the Ecole de Physique des Houches, held in August, 2009. The aim of the event was to familiarize the new generation of PhD students and postdoctoral fellows with the principles and methods of modern lattice field theory, which aims to resolve fundamental, non-perturbative questions about QCD without uncontrolled approximations. The emphasis of the book is on the theoretical developments that have shaped the field in the last two decades and that have turned lattice gauge theory into a robust approach to the determination of low energy hadronic quantities and of fundamental parameters of the Standard Model. By way of introduction, the lectures begin by covering lattice theory basics, lattice renormalization and improvement, and the many faces of chirality. A later course introduces QCD at finite temperature and density. A broad view of lattice computation from the basics to recent developments was offered in a corresponding course. Extrapolations to physical quark masses and a framework for the parameterization of the low-energy physics by means of effective coupling constants is covered in a lecture on chiral perturbation theory. Heavy-quark effective theories, an essential tool for performing the relevant lattice calculations, is covered from its basics to recent advances. A number of shorter courses round out the book and broaden its purview. These included recent applications to the nucleon--nucleon interation and a course on physics beyond the Standard Model\"--Provided by publisher.
Book
The TT¯ deformation of quantum field theory as random geometry
A
bstract
We revisit the results of Zamolodchikov and others on the deformation of two-dimensional quantum field theory by the determinant det
T
of the stress tensor, commonly referred to as
T
T
¯
. Infinitesimally this is equivalent to a random coordinate transformation, with a local action which is, however, a total derivative and therefore gives a contribution only from boundaries or nontrivial topology. We discuss in detail the examples of a torus, a finite cylinder, a disk and a more general simply connected domain. In all cases the partition function evolves according to a linear diffusion-type equation, and the deformation may be viewed as a kind of random walk in moduli space. We also discuss possible generalizations to higher dimensions.
Journal Article
Quantum field theory, as simply as possible
\"Quantum field theory grew out of quantum mechanics in the late 1930s and was developed by a generation of brilliant young theorists, including Julian Schwinger and Richard Feynman. Their predictions were experimentally verified to an astounding accuracy unmatched by the rest of physics. Quantum field theory unifies quantum mechanics and special relativity, thus providing the framework for understanding the quantum mysteries of the subatomic world. With his trademark blend of wit and physical insight, A. Zee guides readers from the classical notion of the field to the modern frontiers of quantum field theory, covering a host of topics along the way, including antimatter, Feynman diagrams, virtual particles, the path integral, quantum chromodynamics, electroweak unification, grand unification, and quantum gravity.\" -- Provided by publisher.
BOOK
Time-reversal breaking in QCD4, walls, and dualities in 2 + 1 dimensions
A
bstract
We study SU(
N
) Quantum Chromodynamics (QCD) in 3+1 dimensions with
N
f
degenerate fundamental quarks with mass
m
and a
θ
-parameter. For generic
m
and
θ
the theory has a single gapped vacuum. However, as
θ
is varied through
θ
=
π
for large
m
there is a first order transition. For
N
f
= 1 the first order transition line ends at a point with a massless
η
′ particle (for all
N
) and for
N
f
>
1 the first order transition ends at
m
= 0, where, depending on the value of
N
f
, the IR theory has free Nambu-Goldstone bosons, an interacting conformal field theory, or a free gauge theory. Even when the 4
d
bulk is smooth, domain walls and interfaces can have interesting phase transitions separating different 3
d
phases. These turn out to be the phases of the recently studied 3
d
Chern-Simons matter theories, thus relating the dynamics of QCD
4
and QCD
3
, and, in particular, making contact with the recently discussed dualities in 2+1 dimensions. For example, when the massless 4
d
theory has an SU(
N
f
) sigma model, the domain wall theory at low (nonzero) mass supports a 3
d
massless
ℂ
ℙ
N
f
−
1
nonlinear
σ
-model with a Wess-Zumino term, in agreement with the conjectured dynamics in 2+1 dimensions.
Journal Article
Partial Compactification of Monopoles and Metric Asymptotics
We construct a partial compactification of the moduli space,
eBook
Statistical Approach to Quantum Field Theory
This book opens with a self-contained introduction to path integrals in Euclidean quantum mechanics and statistical mechanics, and moves on to cover lattice field theory, spin systems, gauge theories and more. Each chapter ends with illustrative problems.
eBook
Quantum simulation of quantum field theories as quantum chemistry
A
bstract
Conformal truncation is a powerful numerical method for solving generic strongly-coupled quantum field theories based on purely field-theoretic technics without introducing lattice regularization. We discuss possible speedups for performing those computations using quantum devices, with the help of near-term and future quantum algorithms. We show that this construction is very similar to quantum simulation problems appearing in quantum chemistry (which are widely investigated in quantum information science), and the renormalization group theory provides a field theory interpretation of conformal truncation simulation. Taking two-dimensional Quantum Chromodynamics (QCD) as an example, we give various explicit calculations of variational and digital quantum simulations in the level of theories, classical trials, or quantum simulators from IBM, including adiabatic state preparation, variational quantum eigensolver, imaginary time evolution, and quantum Lanczos algorithm. Our work shows that quantum computation could not only help us understand fundamental physics in the lattice approximation, but also simulate quantum field theory methods directly, which are widely used in particle and nuclear physics, sharpening the statement of the quantum Church-Turing Thesis.
Journal Article