arXiv subjects

Florian Oppermann

Publications and source records attributed to Florian Oppermann.

4 recordsLinked to original sources

arXiv2023

Mass-ratio dependent strong-field dissociation of artificial helium hydride isotopologues

We study the effect of the nuclear-mass ratio in a diatomic molecular ion on the dissociation dynamics in strong infrared laser pulses. A molecular ion is a charged system, in which the dipole moment depends on the reference point and therefore on the position of the nuclear center of mass, so that the laser-induced dynamics is expected to depend on the mass asymmetry. Whereas usually both the reduced mass and the mass ratio are varied when different isotopologues are compared, we fix the reduced mass and artificially vary the mass ratio in a model system. This allows us to separate effects related to changes in the resonance frequency, which is determined by the reduced mass, from those that arise due to the mass asymmetry. Numerical solutions of the time-dependent Schr\"odinger equation are compared with classical trajectory simulations. We find that at a certain mass ratio, vibrational excitation is strongly suppressed, which decreases the dissociation probability by many orders of magnitude.

physics.atom-ph↗

arXiv2022

The Rough with the Smooth of the Light Cone String

The polynomials in the generators of a unitary representation of the Poincar\'e group constitute an algebra which maps the dense subspace S of smooth, rapidly decreasing wavefunctions to itself. This mathematical result is highly welcome to physicists, who previously just assumed their algebraic treatment of unbounded operators be justified. The smoothness, however, has the side effect that a rough operator R, which does not map a dense subspace of S to itself, has to be shown to allow for some other dense domain which is mapped to itself both by R and all generators. Otherwise their algebraic product, their concatenation, is not defined. Canonical quantization of the light cone string postulates operators $-i X^1$ and $P^- = (P^0 - P^z)/2$ and as their commutator the multiplicative operator R = P^1/(P^0 + P^z). This is not smooth but rough on the negative z-axis of massless momentum. Using only the commutation relations of P^m with the generators $-i M_iz$ of rotations in the $P^i$-$P^z$-plane we show that on massless states the operator $R$ is inconsistent with a unitary representation of SO(D-1). This makes the algebraic determination of the critical dimension, $D=26$, of the bosonic string meaningless: if the massless states of the light cone string admit R then they do not admit a unitary representation of the subgroup SO(D-1) of the Poincar\'e group. With analogous arguments we show: Massless multiplets are inconsistent with a translation group of the spatial momentum which is generated by a self-adjoint spatial position operator $X$.

hep-th↗

arXiv2022

Heisenberg versus the Covariant String

A Poincar\'e multiplet of mass eigenstates $\bigl(P^2 - m^2\bigr)\Psi = 0$ cannot be a subspace of a space with a $D$-vector position operator $X=(X_0,\dots X_{D-1})$: the Heisenberg algebra $[P^m, X_n] = i \delta^m{}_n$ implies by a simple argument that each Poincar\'e multiplet of definite mass vanishes. The same conclusion follows from the Stone-von Neumann theorem. In a quantum theory the constraint of an absolutely continuous spectrum to a lower dimensional submanifold yields zero even if Dirac's treatment of the corresponding classical constraint defines a symplectic submanifold with a consistent corresponding quantum model. Its Hilbert space is not a subspace of the unconstrained theory. Hence the operator relations of the unconstrained model need not carry over to the constrained model. Our argument excludes quantized worldline models of relativistic particles and the physical states of the covariant quantum string. We correct misconceptions about the generators of Lorentz transformations acting on particles.

hep-th↗

arXiv2022

Heisenberg Algebra and String Theory

If the algebra of the Poincar\'e generators is enlarged by the spacetime position operator $X=(X_0,\dots, X_{D-1})$ then the spectra of the momentum $P$ and the mass $P^2$ are unbounded and continuous. In particular, the constraint $(P^2 - m^2)\Psi_{\text{phys}}=0$ of the covariant string has no solution in the space which admits $X$: All physical states vanish, $\Psi_{\text{phys}}=0$. Vice versa, a space spanned by mass eigenstates does not admit the position operator $X$ in $D$ dimensions. A massless particle does not allow a spatial position operator $\vec X$. The domain of Heisenberg pairs $X^i$ and $P^j$, $i,j\in \{1,\dots D-2\}$, $D > 2$, which commute with $P^+=(P^0 + P_z)/\sqrt{2}$, $[P^+,X^i] = 0$, does not allow for a space with massless or tachyonic states, which is mapped to itself by rotations, leave alone Lorentz transformations. This is true in all dimensions and makes the algebraic calculation of the critical dimension, $D=26$, of the bosonic string meaningless: the light cone string is not Lorentz invariant.

hep-th↗