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Abstract Hamiltonian simulations of quantum systems require a finite-dimensional representation of the operators acting on the Hilbert space $$\mathcal {H}$$ H . Here we give a prescription for gauge links and canonical momenta of an SU(2) gauge theory, such that the matrix representation of the former is diagonal in $$\mathcal {H}$$ H . This is achieved by discretising the sphere $$S_3$$ S 3 isomorphic to SU(2) and the corresponding directional derivatives. We show that the fundamental commutation relations are fulfilled up to discretisation artefacts. Moreover, we directly construct the Casimir operator corresponding to the Laplace–Beltrami operator on $$S_3$$ S 3 and show that the spectrum of the free theory is reproduced again up to discretisation effects. Qualitatively, these results do not depend on the specific discretisation of SU(2), but the actual convergence rates do.

Abstract We study the properties of three-body resonances using a lattice complex scalar φ 4 theory with two scalars, with parameters chosen such that one heavy particle can decay into three light ones. We determine the two- and three-body spectra for several lattice volumes using variational techniques, and then analyze them with two versions of the three-particle finite-volume formalism: the Relativistic Field Theory approach and the Finite-Volume Unitarity approach. We find that both methods provide an equivalent description of the energy levels, and we are able to fit the spectra using simple parametrizations of the scattering quantities. By solving the integral equations of the corresponding three-particle formalisms, we determine the pole position of the resonance in the complex energy plane and thereby its mass and width. We find very good agreement between the two methods at different values of the coupling of the theory.

Abstract We test an alternative proposal by Bruno and Hansen (J High Energy Phys 2021(6), https://doi.org/10.1007/JHEP06(2021)043 , 2021) to extract the scattering length from lattice simulations in a finite volume. For this, we use a scalar $$\phi ^4$$ ϕ 4 theory with two mass nondegenerate particles and explore various strategies to implement this new method. We find that the results are comparable to those obtained from the Lüscher method, with somewhat smaller statistical uncertainties at larger volumes.

Introduction: Self-inflicted orchidectomy and auto-castration, also known as “Eshmun complex” is a rare phenomenon. The aim of our study it to present the management of a patient who performed a self orchiectomy and propose a non-systematic review of literature about self-orchiectomy. Material and method: A 27-years old male Patient with psychiatric disorder was admitted to our ward to have been cutted his scrotum with scissors and cut away his left testicle causing active bleeding from the left spermatic artery. The patient underwent emergency surgery with clamping of the spermatic cord and hemostasis of the wound. Results: After surgery the clinical condition of the patient remained good during whole hospitalization. Urgent psychiatric evaluation was performed in order to administer proper therapy for acute management. To best of our knowledge, only 11 cases of self-orchidectomy are reported in literature and all of them except 1 case, underwent surgical exploration. Conclusions: Self-orchidectomy is an extremely rare phenomenon, often associated with psychiatric disorders, compounded by the use of drugs. In our opinion, emergency surgery should be the first choice of treatment, offering diagnostic and hemostatic purpose in a single act, aimed to prevent acute and postacute complications.

Objective: To compare the retroperitoneal with the transperitoneal approach in a series of patients underwent to robotic-assisted pyelolithotomy (RP). Materials and methods: From January 2015 to December 2018 we evaluated 20 patients subjected to robotic pyelolithotomy; 11 patients were treated with retroperitoneal approach (RRP) and 9 with transperitoneal approach (TRP). For each patient intra and perioperative data were recorded: operative time (OT), blood loss (BL), length of hospital stay (LOS), stone clearance, post-operative complications and time to remove the drain. The presence of stone fragments < 4 mm was considered as stone free rate. Results: The principal stone burden was greater in the TRP group than in the RRP group (48 ± 10 mm vs 32 ± 14 mm, p = 0.12). Preoperative hydronephrosis was present in 7 (64%) patients in RRP group and a mild hydronephrosis in 3 of TRP group (p = 0.04). The average operative time was higher in the RRP group than in the TRP group (203 ± 45 min vs 137 ± 31 min, p = 0.002). The average blood loss was 305 ± 175 ml in the RRP group versus 94 ± 104 ml in the TRP group (p = 0.005). The stone free rate was similar between the two groups, 36% (4 patients) in the RRP group and 44% (4 patients) in the TRP (p = 0.966). Conclusions: RP appears to be a safe and effective minimally invasive treatment for some patients with renal staghorn calculi or urinary tract malformations. The TRP may give lower operative time and better results in terms of blood loss and length of hospital stay.

Objective: To present the management of a patient with partial disruption of both cavernosal bodies and complete urethral rupture and to propose a non-systematic review of literature about complete urethral rupture. Material and method - Case report: A 46 years old man presented to our emergency department after a blunt injury of the penis during sexual intercourse. On physical examination there was subcutaneous hematoma extending over the proximal penile shaft with a dorsal-left sided deviation of the penis and urethral bleeding. Ultrasound investigation showed an hematoma in the ventral shaft of the penis with a discontinuity of the tunica albuginea of the right cavernosal corporum. The patient underwent immediate emergency surgery consisted on evacuation of the hematoma, reparation the partial defect of both two cavernosal bodies and end to end suture of the urethra that resulted completely disrupted. Results: The urethral catheter was removed at the 12-th postoperative day without voiding symptoms after a retrograde urethrography. 6 months postoperatively the patients was evaluated with uroflowmetry demonstrating a max flow rate of 22 ml/s and optimal functional outcomes evaluated with validated questionnaires. 8 months after surgery the patients was evaluated by dynamic magnetic resonance (MRI) of the penis showing only a little curvature on the left side of the penile shaft. Conclusion: Penile fracture is an extremely uncommon urologic injury with approximately 1331 reported cases in the literature till the years 2001. To best of our knowledge from 2001 up today, 1839 more cases have been reported, only in 159 of them anterior urethral rupture was associated and in only 22 cases a complete urethral rupture was described. In our opinion, in order to prevent long term complications, in case of clinical suspicion of penile fracture, especially if it is associated to urethral disruption, emergency surgery should be the first choice of treatment.