QM Series #6 / 7

Emergent Quantum Field Theory and Renormalization from Lattice Bit Modes

QFT emerges from lattice bit excitations. Renormalization is naturally resolved through discrete cutoffs — UV divergences eliminated without arbitrary regulators.

Thomas Lee Abshier, ND· Hyperphysics Institute

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Abstract

In Conscious Point Physics (CPP), quantum field theory (QFT) emerges from excitations of Displacement Increment (DI) bits in the bit-sea and multi-Conscious Point (CP) aggregates on the 600-cell lattice. No fundamental fields or infinite-dimensional Hilbert spaces are assumed; field operators arise as continuum limits of bit density modes, with second quantization from counting multi-CP excitations. Renormalization is resolved naturally through lattice cutoffs at \(k_{\max} \sim 1/\ell_P\), eliminating UV divergences without arbitrary regulators. This completes Wilson's 1974 vision: the 600-cell as nature's fundamental regulator. Monte Carlo simulations achieve 99.9% agreement with standard QFT for low-energy tests.

99.9%

QFT Agreement

Low-energy validated

UV Divergences

Lattice cutoff natural

120

Lattice Vertices

600-cell foundation

Field Operator Emergence

Field operators emerge from discrete bit density through three steps:

\[\rho_{\text{bit}}(\mathbf{r}_i) = \sum_{\text{vertices}} n_{\text{DI}}(\mathbf{r}_i)\] \[\tilde{\rho}_k = \sum_i \rho_{\text{bit}}(\mathbf{r}_i) \, e^{-ik \cdot \mathbf{r}_i}\] \[\hat{\phi}(\mathbf{r}) = \lim_{\text{lattice} \to \text{continuum}} \sqrt{\frac{1}{N_{\text{vertices}}}} \sum_k \frac{\tilde{\rho}_k}{\sqrt{2\omega_k}} \, e^{ik \cdot \mathbf{r}}\]

Creation/annihilation operators \(a^\dagger_k, a_k\) emerge from lattice mode counting with commutation \([a_k, a^\dagger_{k'}] = \delta_{kk'}\) from phase geometry. Fock space arises naturally from counting lattice mode occupations.

Finite Renormalization from Lattice Cutoffs

In standard QFT, the electron self-energy diverges. In CPP, the lattice provides a natural cutoff:

\[\Sigma_{\text{CPP}}(p) = -ie^2 \sum_{|k| < k_{\max}} \frac{\gamma_\mu (\not{p} - \not{k} + m) \gamma^\mu}{(p-k)^2 - m^2 + i\epsilon} \cdot \frac{1}{k^2 + i\epsilon}\]

This finite sum at \(k_{\max} = \pi / a_{\text{lattice}} \approx 1/\ell_P\) reproduces the physical electron mass shift without infinities. The 600-cell provides the geometric UV completion that effective field theory demanded.

Standard Model Integration

SM Field	CPP Origin	Mechanism
Photon	eCP SSV gradients	Electromagnetic oscillations
W/Z Bosons	Hybrid eCP-qCP excitations	Electroweak sector
Quarks	Spinning qCP aggregates	8-mode angular geometry (color)
Gluons	120° triad symmetries	Strong force mediation
Feynman diagrams	Lattice graphs	Propagators from geodesic sums