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Details of Grant 

EPSRC Reference: EP/V002821/1
Title: PT symmetric field theory
Principal Investigator: Sarkar, Professor S
Other Investigators:
Ellis, Professor J Alexandre, Dr JF Mavromatos, Professor N
Researcher Co-Investigators:
Project Partners:
Department: Physics
Organisation: Kings College London
Scheme: Standard Research
Starts: 01 July 2021 Ends: 30 June 2024 Value (£): 477,769
EPSRC Research Topic Classifications:
Mathematical Physics
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
31 Aug 2020 EPSRC Mathematical Sciences Prioritisation Panel September 2020 Announced
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


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.

Key Findings
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