| EPSRC Reference: |
EP/V002821/1 |
| Title: |
PT symmetric field theory |
| Principal Investigator: |
Sarkar, Professor S |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Physics |
| Organisation: |
Kings College London |
| Scheme: |
Standard Research |
| Starts: |
01 July 2021 |
Ends: |
31 October 2024 |
Value (£): |
477,769
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
Physical systems are described by a quantity called the Hamiltonian. In conventional
quantum physics two kinds of Hamiltonians are used,
(i) Hermitian Hamiltonians, which govern the behaviour of isolated
systems, and (ii) non-Hermitian Hamiltonians, which have been used to describe
the behaviour of systems in contact with the environment.
Hermitian Hamiltonians describe idealised systems in equilibrium whose total
energy and probability are conserved; the energy levels of such systems are real.
Non-Hermitian Hamiltonians in general receive energy from and/or dissipate energy
into their environment, so they are not typically in equilibrium, their energy and
probability are not conserved, and their energy levels are complex, due to the levels being unstable.
This proposal concerns a category of so-called PT-symmetric
Hamiltonians, which share properties of both Hermitian and non-Hermitian
Hamiltonians, being intermediate between conservative and dissipative systems.
Like non-Hermitian systems,PT-symmetric systems are not isolated, but their contact
with the environment is constrained so that gain from the environment
and loss to the environment are exactly balanced. Thus, while they
are not isolated, PT-symmetric systems in equilibrium behave
like Hermitian systems and their energy levels are real. However,
unlike Hermitian systems, PT-symmetric systems can exhibit
a transition from an unbroken equilibrium phase, where the energies
are real, to a broken nonequilibrium phase where the energies are
complex. Hermitian systems can never have complex energies and thus
cannot have such a phase transition. The PT phase transition is a characteristic
signature that has been observed in experiments.
Quantum mechanics is essential for describing the physics of particles and involves a
finite number of degrees of freedom. However, particles are excitations of quantum fields,
which are defined over all space and time. Quantum field theories
have infinitely many degrees of freedom. Consequently the formulation of PT-symmetric
field theory is required to describe any fundamental theory involving PT symmetry.
Moreover, even within the framework of Hermitian quantum field theories, non-Hermitian
PT symmetric features often emerge in calculations. These features tend to be dismissed,
either on the basis of nonrigorous mathematics related to prescriptions introduced to extract
finite numbers from divergent expressions in calculations,
or incompleteness of the physical model. This proposal investigates directly the role and
properties of PT symmetry in fundamental quantum field theories by investigating the following
questions:
1. Are there analogues in quantum field theory of the features that distinguish PT-symmetric
quantum mechanical systems from Hermitian quantum mechanics?
2.Are there any restrictions on the type of PT-symmetric field theories that show analogous features?
3. Can non-Hermitian features, which arise due to divergences in Hermitian field theories, be dealt
with by procedures within the framework of PT-symmetric quantum field theory?
4. Can PT-symmetric field theories lead to new possibilities for models of fundamental physics, which,
in low number of spatial dimension, may be realised in the laboratory?
These are the questions that the project aims to answer.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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