A Why are we allowed to use the trace cyclicity here?

  • A
  • Thread starter Thread starter Heidi
  • Start date Start date
  • Tags Tags
    Trace
Heidi
Messages
420
Reaction score
40
TL;DR Summary
trace cyclicity with operators?
Hi Pf
i am reading this article: pillet.univ-tln.fr/data/pdf/KMS-states.pdf
I know that the trace cyclicity can be used when there is a product of matrices. But here we have operators (an hamiltonian , an operator which can be the position operators) . the author take the trace of a product. is this product trace class? are we allowed to use the cyclicity formula of the trace here?
thanks.
 
Physics news on Phys.org
The operators are bounded because the Hilbert space is finite-dimensional. So we're talking here about finite matrices.
 
yes but my question is more general. Consider 2 operators A and B on an infinite dimensional Hilbert space. If the products AB and BA are class trace it is meaningful to consider Tr(AB) and Tr(BA)
Are there conditions on these operators so that trace cyclicity is true.
Qft is on infinite dimensional hilbert spaces and exp(-H) often appears as one of the operators in the trace.
 

Thread 'Prof Mike Wiest's proposed link between quantum and consciousness'

I am not sure if this belongs in the biology section, but it appears more of a quantum physics question. Mike Wiest, Associate Professor of Neuroscience at Wellesley College in the US. In 2024 he published the results of an experiment on anaesthesia which purported to point to a role of quantum processes in consciousness; here is a popular exposition: https://neurosciencenews.com/quantum-process-consciousness-27624/ As my expertise in neuroscience doesn't reach up to an ant's ear...
View full post »

Thread 'Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
View full post »

Thread 'Is It Known For Sure Infinites In QFT Are Caused Using a Continuum?'

I am reading WHAT IS A QUANTUM FIELD THEORY?" A First Introduction for Mathematicians. The author states (2.4 Finite versus Continuous Models) that the use of continuity causes the infinities in QFT: 'Mathematicians are trained to think of physical space as R3. But our continuous model of physical space as R3 is of course an idealization, both at the scale of the very large and at the scale of the very small. This idealization has proved to be very powerful, but in the case of Quantum...
View full post »

Similar threads

A How can we measure these Hermitian operators?
Replies
9
Views
2K
Mathematical Quantum Statistics: Why is A*rho of trace class?
Replies
1
Views
2K
I Are density matrices part of a real vector space?
Replies
9
Views
2K
Density Operators, Trace and Partial Trace
Replies
2
Views
6K
Trace Distance in quantum mechanics
Replies
1
Views
2K
A Understanding the Use of Trace in QFT Lagrangian for Chiral Symmetry in QCD
Replies
1
Views
3K
Questions about the Casimir energy equation
Replies
1
Views
1K
Density matrix formalism and Poincaré invariance
Replies
17
Views
2K
A Why we can perform normal ordering?
Replies
4
Views
2K
A Does Bell's theorem imply nonlocality using a false assumption
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top