Ladder operators with no vacuum, their coherent states, and an application to graphene

• URL: http://arxiv.org/abs/2401.12239v1
• Date: Fri, 19 Jan 2024 20:22:34 GMT
• Title: Ladder operators with no vacuum, their coherent states, and an application to graphene
• Abstract summary: In this paper we discuss what happens when considering lowering operators with no vacua. We propose a possible construction of coherent states, and we apply our construction to graphene.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In literature ladder operators of different nature exist. The most famous are those obeying canonical (anti-) commutation relations, but they are not the only ones. In our knowledge, all ladder operators have a common feature: the lowering operators annihilate a non zero vector, the {\em vacuum}. This is connected to the fact that operators of these kind are often used in factorizing some positive operators, or some operators which are { bounded from below}. This is the case, of course, of the harmonic oscillator, but not only. In this paper we discuss what happens when considering lowering operators with no vacua. In particular, after a general analysis of this situation, we propose a possible construction of coherent states, and we apply our construction to graphene.

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